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Dashpot
Dashpot
Dashpot
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Diagramatic symbol used to represent a dashpot.

A dashpot, also known as a damper[citation needed], is a mechanical device that resists motion via viscous damping.[1] The resulting force is proportional to the velocity, but acts in the opposite direction,[2] slowing the motion and absorbing energy. Kinetic energy is converted to heat. It is commonly used in conjunction with a spring.

Types

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The two most common types of dashpots are linear and rotary.

Linear dashpot

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Simplified diagram
of a linear dashpot.

Linear dashpots — or linear dampers — are used to exert a force opposite to a translation movement. They are generally specified by stroke (amount of linear displacement) and damping coefficient (force per velocity).

Rotary dashpot

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Similarly, rotary dashpots will tend to oppose any torque applied to them, in an amount proportional to their rotational speed. Their damping coefficients will usually be specified by torque per angular velocity. One can distinguish two kinds of viscous rotary dashpots:[3]

  • Vane dashpots which have a limited angular range but provide a significant damping torque. The damping force is the result of one or multiple vanes moving through a viscous fluid and letting it flow via calibrated openings.
  • Continuous rotation dashpots which aren't limited in their rotation angle but provide a smaller damping coefficient. These use the friction generated by the shearing forces induced in the viscous fluid itself by the difference in motion between the dashpot's rotor and stator.

Eddy current damper

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A less common type of dashpot is an eddy current damper, which uses a large magnet inside a tube constructed of a non-magnetic but conducting material (such as aluminium or copper). Like a common viscous damper, the eddy current damper produces a resistive force proportional to velocity. A common use of the eddy current damper is in balance scales. This is a frictionless (while near rest) method that allows the scale to quickly come to rest.[4][5][6][7]

One-way operation

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Dashpots frequently use a one-way mechanical bypass to permit fast unrestricted motion in one direction and slow motion using the dashpot in the opposite direction. This permits, for example, a door to be opened quickly without added resistance, but then to close slowly using the dashpot. For hydraulic dashpots this unrestricted motion is accomplished using a one-way check-valve that allows fluid to bypass the dashpot fluid constriction. Non-hydraulic rotatory dashpots may use a ratcheting gear to permit free motion in one direction.

Theory

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Dashpots are frequently used to add damping to dynamic systems. When designing and analyzing systems, dashpots are often assumed to be linear, meaning that their output force F is linearly proportional to their velocity v. The direction of the force is opposite the velocity, giving the negative sign in the equation below, and the constant of proportionality often uses the symbol c.

This permits convenient analysis of systems such as harmonic oscillators. However, the behavior of real-world dashpots is frequently non-linear, meaning that the force is proportional to the velocity raised to some exponent α, which can vary between 0.2 and 2.0.[8]

Different exponents are better suited for different applications, but exponents other than 1 must be analyzed with numeric methods instead of calculus. Systems that use non-linear dampers (any exponent other than 1) are much more time-consuming to design and analyze than linear dampers.

Applications

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Dashpot in a Zenith-Stromberg carburetor

A dashpot is a common component in a door closer to prevent it from slamming shut. A spring applies force to close the door, which the dashpot offsets by forcing fluid to flow through an orifice, often adjustable, between reservoirs, which slows the motion of the door.

Consumer electronics often use dashpots where it is undesirable for a media access door or control panel to suddenly pop open when the door latch is released. The dashpot provides a steady, gentle motion until the access door has fully opened.

Dashpots are a key component in shock absorbers, used to cushion a vehicle against vibrations caused by an uneven road surface.[9]

They are also used on carburetors, where the return of the throttle lever is cushioned just before the throttle fully closes, then is allowed to fully close slowly to reduce emissions. The British SU carburettor's main piston carries a stepped needle. This needle is held in the fuel flow orifice. The manifold vacuum causes this piston to rise allowing more fuel into the airflow. The SU's dashpot has a fixed hydraulic piston, damping the main piston as it moves upward. A valve in the piston disables the damping as the main piston returns.

Large forces and high speeds can be controlled by dashpots. For example, they are used to arrest the steam catapults on aircraft carrier decks.

Relays can be made to have a long delay by utilizing a piston filled with fluid that is allowed to escape slowly. Electrical switchgear may use dashpots in their overcurrent sensing mechanism to reduce reaction speed to brief events, thus making them less sensitive to false-triggering during transients whilst still remaining sensitive to sustained overloads. Another use is for delaying the closing or opening of an electrical circuit. Such a dashpot timer might be used for example for timed staircase lighting.

Anti-stall mechanisms in internal combustion engines are aimed to prevent stalling of the engine at low rpm. Anti-stall mechanisms use dashpots to arrest the final closing movement of the throttle.

Large dashpots are added to bridges and buildings to protect against earthquakes and wind vibrations.[10] One classic example of this use is the repairs made to the Millennium Bridge in London after it was found to wobble when walked on.[11]

Viscoelasticity

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Dashpots are used as models of materials that exhibit viscoelastic behavior, such as muscle tissue. Maxwell and Kelvin–Voigt models of viscoelasticity use springs and dashpots in series and parallel circuits respectively. Models containing dashpots add a viscous, time-dependent element to the behavior of solids, allowing complex behaviors like creep and stress relaxation to be modeled.

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Dashpot

View on Grokipedia
from Grokipedia
A dashpot is a mechanical device designed to resist motion through viscous , providing a force that is directly proportional to the relative velocity between its components, typically achieved via a moving within a filled with a viscous fluid or gas. In operation, the dashpot functions as an impedance element analogous to a in electrical circuits, where the damping force f(t)=μv(t)f(t) = \mu v(t) opposes the piston's motion, with μ\mu as the damping constant and v(t)v(t) as the ; this dissipates as through shear or orifice flow, thereby controlling speed, reducing vibrations, and cushioning impacts without storing energy. Dashpots are classified into linear types, which handle translational motion, and rotary types for angular motion, with further variations including hydraulic models using oil or other liquids for higher force capacities and pneumatic models employing air for lighter-duty, precise control in applications requiring adjustable damping. Commonly applied in automotive shock absorbers to smooth road impacts, door closers for gradual operation, and industrial machinery to manage oscillatory forces, dashpots have historical roots in 19th-century innovations, such as George Corliss's valve gear in the 1840s and William S. Burroughs's 1888 adding machine patent.

Fundamentals

Definition and Purpose

A dashpot is a mechanical device that provides viscous by resisting motion with a force proportional to the of the moving component, thereby converting into through or analogous mechanisms. The primary purpose of a dashpot is to slow or stabilize moving parts in mechanical systems, prevent unwanted oscillations, and ensure controlled deceleration, particularly in applications where sudden stops could lead to structural damage or instability. Typically, a dashpot consists of a operating within a fluid-filled , where the piston's movement displaces the viscous through restricted passages, generating the resistive . The damping coefficient, denoted as cc, quantifies this resistance and has units of N·s/m for linear configurations, reflecting the per unit . Unlike elastic elements such as springs that store , a dashpot dissipates entirely as through the work performed against the viscous , without any . Dashpots are essential in diverse contexts, from automotive suspensions to precision machinery, with variants such as linear and rotary forms adapted to specific types of motion.

Historical Development

The need for mechanisms in mechanical systems emerged in the late 18th century, particularly with James Watt's invention of the in 1788 for regulating speed, which highlighted the requirement for oscillation control though initial designs lacked dedicated dampers. Practical dashpots, hydraulic devices using viscous resistance to slow motion, were first developed in the early for to address valve slamming and governor instability. In 1842, American inventor Frederick E. Sickels patented the first effective dashpot (U.S. Patent No. 2,631) as part of a cutoff mechanism, enabling controlled closure in and marking a key advancement in industrial machinery. This was further advanced in 1849 by George H. Corliss, who patented an improved for steam engines that incorporated dashpots to precisely control valve opening and closing, enhancing efficiency and reducing vibration in industrial applications. By the mid-19th century, dashpots found application in transportation, with early fluid-filled designs integrated into railway buffers to absorb shocks during coupling and deceleration. Spring-loaded buffers appeared on the & Manchester Railway in the 1830s, while hydraulic variants for inter-car buffers emerged in the mid-20th century for enhanced energy dissipation; hydraulic buffer stops at track ends were described in engineering papers as early as the 1880s. In automotive contexts, the transition to fluid-based damping occurred around 1907 when Claude H. Foster of the Gabriel Company introduced the "Snubber," an early friction damper, followed by the first hydraulic in 1918, which utilized piston-cylinder arrangements for vehicle suspension control. During , dashpots advanced significantly in through oleo-pneumatic struts, patented by Armstrong in 1915, which combined oil damping with air compression to cushion impacts on rough . Post-1940s refinements focused on viscous fluids for precision applications, including electromagnetic relays where dashpots provided timed delays in switching operations, improving reliability in early electronics. In recent decades up to 2025, dashpot evolution has incorporated and electromagnetic principles for adaptive performance, notably dampers using fluids that change under magnetic fields. MR fluids were pioneered by Jacob Rabinow in 1948, but practical dampers emerged in the , with Delphi's 2002 automotive application in the enabling real-time damping adjustment for improved handling. These variants have extended to and electric vehicles, where electromagnetic and MR systems provide variable control for stabilization in dynamic environments, including integrations with for enhanced vehicle performance.

Types

Linear Dashpots

Linear dashpots resist linear translational motion by employing a piston-cylinder arrangement filled with a viscous fluid, such as hydraulic oil or silicone oil, which generates opposition through fluid displacement as the piston moves relative to the cylinder. The piston's motion forces the fluid through restricted pathways, creating a damping effect proportional to velocity. The operational range is determined by the stroke length, typically spanning 10 to 500 mm to accommodate various mechanical requirements in translational systems. Pneumatic linear dashpots use air or gas as the medium instead of liquid, providing low-friction operation suitable for precision applications. In these designs, the displaces air through orifices or porous materials, offering adjustable with minimal and no risk of leakage, ideal for clean environments and lighter loads. The force in these devices directly opposes the linear velocity of the , providing controlled resistance that is quantified by the coefficient c, expressed in units of newton-seconds per meter (N·s/m). This characteristic makes linear dashpots well-suited for applications involving reciprocating motions, such as in or linear slides in automated machinery, where smooth deceleration and reduction are essential. Construction of linear dashpots varies to meet needs, with orifice-controlled designs offering fixed resistance via a constant for predictable , while variable-area configurations enable adjustment through mechanisms like needle valves to fine-tune fluid flow and thus the rate. Cylinders are commonly constructed from durable to withstand pressures and wear, paired with seals that ensure fluid containment and flexibility during movement. These dashpots provide high precision in , particularly for short strokes where accurate regulation is critical, enhancing stability in dynamic systems. A key limitation is gradual fluid leakage over time, arising from seal degradation and piston clearances, which can reduce effectiveness and necessitate periodic (less relevant for pneumatic variants). Unlike rotary dashpots suited to angular systems, linear variants excel in straight-line applications.

Rotary Dashpots

Rotary dashpots are mechanical devices engineered to provide controlled opposition to angular motion through viscous shear forces. In their fundamental design, a vane or paddle attached to a rotating shaft is immersed in a viscous , typically , contained within a cylindrical . As the shaft rotates, the vane displaces the , generating a that is proportional to the and acts to dampen the motion. These devices are categorized into two primary subtypes based on their operational range and torque capabilities. Vane-type rotary dashpots feature a vane that rotates within fixed compartments, offering high for limited angular displacements, typically ranging from 60° to 240°, making them ideal for applications involving reciprocating or partial rotations. In contrast, continuous rotation dashpots employ a or that shears layers across concentric surfaces, providing lower torque coefficients suitable for full 360° motion without angular restrictions. The performance of rotary dashpots is characterized by their damping coefficient, expressed in N·m·s/rad, which quantifies the per unit . This coefficient is tuned by selecting fluids with specific viscosities, such as oils ranging from 350 to 500,000 cSt, to achieve desired outputs; for instance, vane types can deliver coefficients up to 960 N·m·s/rad, while continuous types typically range from 0.2 to 20 N·m·s/rad. Construction emphasizes durability and reliability, with sealed housings that are vacuum-filled to prevent fluid leaks and eliminate the need for . These housings often incorporate bearings, such as miniature ball races or anti-friction bushes, to ensure smooth shaft rotation. Materials commonly include aluminum or zinc alloy for the body to balance weight and strength, paired with stainless or mild shafts, and robust seals like or PTFE-reinforced types to maintain integrity across variations (e.g., 0°C to 60°C for commercial models or -30°C to +50°C for specialized applications). Rotary dashpots find application in systems requiring precise angular control, such as pneumatic actuators or door hinges.

Eddy Current Dampers

Eddy current dampers function as non-contact dashpots by leveraging to generate damping forces. In this mechanism, a permanent or moves relative to a stationary conductive, non-magnetic material, such as a tube or plate, inducing circulating within the conductor. These create an opposing according to , which resists the relative motion and dissipates primarily as . The resulting damping force is proportional to the velocity of the moving component and the square of the strength, mimicking viscous damping without physical contact or friction. The design typically features a moving magnetic assembly—often an array of permanent with alternating polarities—positioned within or adjacent to a conductive . For linear eddy current dampers, the may traverse a cylindrical tube, while plate-based designs involve a sliding parallel to a flat aluminum conductor. Rotary variants adapt this principle using rotating arrays near annular conductive rings. Electromagnets can supplement permanent to adjust field strength dynamically, enhancing adaptability for applications like . Construction emphasizes high-conductivity, non-magnetic materials to optimize generation and minimize losses. Copper tubes or windings provide excellent conductivity for the stationary conductor, paired with aluminum plates in simpler plate-type setups for cost-effectiveness and lightweight properties. Permanent magnets, such as neodymium-iron-boron (NdFeB), generate the required field, often mounted on a shaft or with pole pieces to concentrate . These dampers support both linear and rotary configurations, with no seals or fluids required, though some designs incorporate circuits like rectifiers and capacitors to harvest induced . Performance is temperature-sensitive, as rising temperatures increase the conductor's resistivity, reducing magnitude and effectiveness; specialized designs using magnetic shunts can mitigate this sensitivity. Key characteristics include frictionless operation, enabling smooth motion in precision environments, and a that scales linearly with but remains lower than fluid-based dashpots, typically ranging from 40 to 124 N·s/m in optimized prototypes. Unlike viscous systems, they require no maintenance or , offering consistent performance over wide speed ranges without . However, the damping force can vary with and gap distance between the and conductor. Advantages of eddy current dampers include their suitability for clean, contamination-sensitive settings such as laboratories and systems, where they provide reliable, low-noise without mechanical wear or pollution. High reliability stems from the absence of contact, supporting long and minimal . Limitations encompass comparatively modest coefficients relative to hydraulic alternatives, potential demagnetization of permanent s under extreme conditions, and sensitivity to temperature fluctuations, which can degrade performance in high-heat environments unless compensated. Additionally, achieving high densities often requires careful optimization of and conductor thickness to counter inherent volume demands.

Operational Modes

Bidirectional Damping

Bidirectional damping in dashpots refers to the symmetric resistance provided against motion in both directions, typically achieved through mechanisms that generate opposing forces proportional to without directional preference. In viscous fluid-based systems, such as those employing symmetrical hydraulic cylinders, the piston movement displaces through unrestricted orifices or flow paths, creating shear resistance that equally opposes extension and compression. This setup ensures controlled speeds in either direction by relying on the fluid's to dissipate uniformly. Eddy current dashpots offer a non-contact alternative, where a conductive element moves relative to a , inducing currents that produce Lorentz forces opposing the motion bidirectionally. The 's reversibility in effect—due to the velocity-dependent nature of the induced currents—allows symmetric without mechanical , making it suitable for precision applications. Examples include piston-style viscous dashpots in industrial machinery and eddy current setups in systems, both designed with balanced flow paths or field configurations to avoid bias. Performance in bidirectional damping is characterized by a constant coefficient across directions, enabling effective control of oscillations in spring-mass systems or stabilizers by reducing without altering equilibrium positions. This uniformity contrasts with unidirectional modes by lacking any preferential allowance for motion in one direction. In practice, such dashpots maintain proportional resistance to , ensuring stable over repeated cycles. Tuning bidirectional dashpots involves adjusting parameters to achieve balanced opposition, such as varying orifice size in viscous models to control flow rates or modulating strength in designs to alter force magnitude. For instance, equal forces for extension and compression can be fine-tuned via external valves or adjustments, optimizing the system for specific load conditions while preserving .

Unidirectional Damping

Unidirectional damping in dashpots enables rapid motion in while providing controlled resistance in the opposite direction, a feature often termed one-way operation. This asymmetry modifies symmetric bidirectional by integrating directional control elements, allowing free movement in the non-damped direction. The primary mechanism involves s, ratchets, or asymmetric paths to selectively. In hydraulic and pneumatic variants, a one-way —such as an umbrella-type or plug-mounted —permits or gas to flow freely through a port during extension or , while restricting it to a narrow orifice during compression or exhaust, generating viscous resistance only in the damped direction. For rotary dashpots, a one-way integrated into the rotor allows free rotation in one sense by disengaging transmission, while viscous shearing of provides in the reverse sense. Mechanical ratchets, used in dry-operation systems, employ pawls and toothed racks to engage under tension for while offering negligible resistance in compression, as seen in seismic fuse mechanisms. Representative examples include hydraulic door closers, where the mechanism allows quick manual opening with minimal resistance but slows automatic closing via restricted fluid flow. Pneumatic dashpots with one-way ports, often filled with , facilitate fast reset motions in timing devices like parking meters. In terms of performance, force applies exclusively in the restricted direction, with near-zero resistance in the free direction, ensuring efficient energy control without impeding intended motions; this is particularly valuable in devices requiring rapid activation followed by controlled deceleration. Variations encompass mechanical ratchets for friction-based dry operation, which lock progressively under load for tension-only response, and fluid-bypass systems in hydraulic designs for viscous control. Some configurations feature adjustable thresholds, such as variable orifice sizes or pawl engagement forces, to tune the release speed in the damped direction.

Theory

Damping Force Models

The for the damping force in a viscous dashpot is expressed as F=−cv,F = -c v, where cc is the damping coefficient and vv is the between the moving parts, such as the and . The damping coefficient cc has units of N·s/m for translational dashpots or N·m·s/ for rotary dashpots, reflecting the proportional resistance to motion. This relation derives from Newton's law of viscosity, which posits that the τ\tau in the is proportional to the gradient: τ=μdudy\tau = \mu \frac{du}{dy}, with μ\mu as the dynamic . In a dashpot, the piston's motion creates a gradient across the or gap, and integrating the resulting shear forces over the contact surface yields the total force F=−cvF = -c v. For cylindrical piston dashpots, the damping coefficient is given by c=6πμLC3c = \frac{6 \pi \mu L}{C^3}, where μ\mu is the fluid viscosity, LL is the piston length, and CC is the radial clearance. The damping process dissipates as via viscous . The instantaneous power dissipated is P=F⋅v=cv2P = F \cdot v = c v^2, and the cumulative heat generation is Q=∫P dt=∫cv2 dtQ = \int P \, dt = \int c v^2 \, dt. These models assume an incompressible fluid and , applicable under low Reynolds numbers (typically Re < 2000) to ensure the linear proportionality holds without turbulent effects.

Linear and Nonlinear Analysis

The nonlinear damping force in dashpots extends the basic linear model by incorporating velocity-dependent variations, commonly expressed as F=−c∣v∣α\sgn(v)F = -c |v|^{\alpha} \sgn(v), where cc is the damping coefficient, vv is the relative velocity, and α\alpha (typically ranging from 0.2 to 2.0) captures phenomena like turbulence or variable geometry in the damper. This formulation reduces to the linear case when α=1\alpha = 1, but deviates for other values to reflect real-world behaviors. Analyzing nonlinear dashpot dynamics poses challenges due to the absence of closed-form analytical solutions, especially in coupled spring-dashpot systems where the equations of motion become intractable. Numerical integration methods, such as the Runge-Kutta approach, or series approximations are essential for solving these differential equations and predicting system responses over time. In high-speed applications involving turbulent fluid flow, such as certain hydraulic isolators, α≈2\alpha \approx 2 prevails, yielding quadratic damping that scales force with the square of velocity for enhanced energy dissipation. Tools like MATLAB/Simulink facilitate accurate simulations of these behaviors through dedicated blocks for nonlinear damper parameterization. Several factors contribute to nonlinearity beyond the exponent α\alpha, including fluid cavitation, which disrupts laminar flow and modifies damping output at elevated velocities. Temperature variations also play a key role, as dynamic viscosity μ\mu in the damping fluid decreases with increasing temperature—often exponentially—altering the effective damping coefficient.

Modeling and Advanced Concepts

Viscoelasticity in Materials

Viscoelastic materials display a combination of viscous and elastic properties, where the viscous component is modeled by a dashpot that dissipates energy through friction-like resistance proportional to strain rate, while the elastic component is represented by a spring that stores energy reversibly. This dual behavior leads to time-dependent responses such as creep (deformation under constant stress) and stress relaxation (decrease in stress under constant strain), which are critical for understanding materials like polymers and biological tissues. The Maxwell model consists of a spring and dashpot connected in series, where the total strain is the sum of the elastic strain in the spring and the viscous strain in the dashpot, allowing the material to exhibit both instantaneous elastic deformation and long-term viscous flow. In this configuration, the constitutive equation is ϵ˙=σ˙E+ση\dot{\epsilon} = \frac{\dot{\sigma}}{E} + \frac{\sigma}{\eta}, where EE is the elastic modulus, η\eta is the viscosity, σ\sigma is stress, and ϵ\epsilon is strain. The characteristic relaxation time is given by τ=ηE\tau = \frac{\eta}{E}, which quantifies the time scale over which stress relaxes under constant strain. For creep under constant stress σ0\sigma_0, the creep compliance is J(t)=1E+tηJ(t) = \frac{1}{E} + \frac{t}{\eta}, reflecting unbounded deformation over time. In contrast, the Kelvin-Voigt model features a spring and dashpot in parallel, where the strain is identical across both elements, but the total stress is shared between the elastic recovery of the spring and the viscous resistance of the dashpot. The constitutive relation is σ=Eϵ+ηϵ˙\sigma = E \epsilon + \eta \dot{\epsilon}, capturing delayed elastic response without instantaneous viscous flow. The retardation time is also τ=ηE\tau = \frac{\eta}{E}, governing the approach to equilibrium strain. These dashpot-based models are applied to simulate the behavior of polymers, where chain entanglements and segmental motion lead to viscoelastic effects under load. In biological tissues, such as muscle, the Kelvin-Voigt model represents the parallel arrangement of contractile fibers (elastic) and fluid-filled extracellular matrix (viscous), enabling accurate prediction of time-dependent deformation during contraction and relaxation. Furthermore, these models are integrated into finite element analysis to evaluate stress distribution in viscoelastic materials, facilitating the design of polymer components and tissue-engineered scaffolds by accounting for rate-dependent material responses.

Integration with Springs

Dashpots are frequently integrated with springs in mechanical systems to provide controlled oscillation damping, where the dashpot's viscous resistance complements the spring's elastic restoring force, resulting in dynamic responses that can be critically damped, underdamped, or overdamped depending on the relative strengths of the components. This combination forms the basis of many vibration isolation systems, analogous to the Kelvin-Voigt viscoelastic model in which a spring and dashpot operate in parallel to model material creep resistance. The governing equation for a mass-spring-dashpot system, assuming linear viscous damping and no external forcing, is given by my¨+cy˙+ky=0,m \ddot{y} + c \dot{y} + k y = 0, where mm is the mass, kk is the spring constant, cc is the damping coefficient of the dashpot, yy is the displacement, and dots denote time derivatives. The system's behavior is characterized by the damping ratio ζ=c2km\zeta = \frac{c}{2 \sqrt{km}}
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