# What is a damping. Text books say damping is proportional to velocity.

1. Jun 10, 2005

### chandran

What is a damping. Text books say damping is proportional to velocity. Why not damping is proportional force? or why not damping proportional to some other parameter. What does damping actually do ? Is there any practical
application ?

2. Jun 10, 2005

Practical applications!!

I race motorcycles - try doing that with no damping in the suspension! If the damping fails, the wheels bounce up and down like you wouldn't believe and the bike is unraceable.

The applications are really too numerous to list, but vehicle suspension is a good one. Even some bridges (London's Millenium bridge) use damping.

3. Jun 10, 2005

### FredGarvin

In most cases, a dampener is a piston, chamber and a fluid. In the direction of movement, the fluid is forced through a small orifice. This produces a restraining force against the direction of motion. The resistance comes from the back pressure created by forcing the fluid through the orifice. That will be a function of not only the speed of the motion, but the density of the fluid and the size of the orifice.

A very common application is the dampener on your screen door. There is an adjustment on it to control the rate of dampening. With that adjustment you are changing the orifice effective area.

You can find more information if you look under the term "dashpot."

4. Jun 10, 2005

### krab

Damping is just a form of friction. Friction converts an organized form of energy into heat. It can be a constant (as in a tire against a road), proportional to velocity (as in shock absorbers), or proportional to velocity squared (as in turbulent losses). Usually only the middle one is called damping.

5. Jun 10, 2005

I never knew that Krab - thanks.

6. Jun 10, 2005

### Stingray

To add a little practical detail, most dampers exert forces which are functions mainly of velocity, although that function is usually nonlinear. Automotive dampers can often be modelled as piecewise functions which become linear for large velocities (although they have very different slopes for positive and negative velocity). The lower-velocity function is usually quadratic (again, it is completely different depending on the direction of motion). A simpler damper would leave the car either uncontrollable or so stiff as to be literally painful to drive. The precise forms of these curves have a huge effect on a car's overall feel and performance.

7. Jun 13, 2005

### SGT

More generally, damping is caused by any element that dissipate energy into heat. In an electrical circuit, damping is provided by the resistive components. In a mechanical system, damping is provided by friction.

8. Jun 13, 2005

### Andrew Mason

Damping refers to the force that limits the amplitude of a vibration - a simple harmonic oscillation.

The solution to a second order differential equation without a first order term is constant amplitude simple harmonic motion. So if the 'damping' were to be proportional to force, or acceleration, the 'damping force' would simply modify the co-efficient of the second order term. The character of the motion would not change - it would still be constant amplitude sinusoidal motion.

Only by adding a first order term - ie. proportional to the first time derivative of position or velocity - does the amplitude of the vibration diminish with time.

AM

9. Jun 14, 2005

### Gokul43201

Staff Emeritus
A damped, driven oscillator is described by the equation :

$$m \ddot{x} - c \dot{x} - kx = f_0 sin(\omega_0 t + \phi)$$

Here, c is called the damping coefficient, and accounts for dissipation in a non-ideal spring.

10. Jun 14, 2005

### Andrew Mason

The solution of which is a function of arbitrarily large amplitude as c approaches 0 (assuming the forcing frequency $\omega_0$ is the natural frequency of the oscillator $\sqrt{k/m}$). Hence, c is the damping coefficient. It prevents the amplitude from becoming arbitrarily large.

AM

11. Jun 14, 2005

### SGT

The forcing function does not need to be sinusoidal. A step function or a dirac delta function can initiate oscillations that are damped only if c is not zero. The equation should read:
$$m \ddot{x} - c \dot{x} - kx = f(t)$$
By the way, the damping acts only on the natural oscilations. The response to the forcing sinusoid is another sinusoid of the same frequency but different phase and amplitude, but that amplitude is maintained without damping.
Also the oscillation can originate from a RLC circuit, where the resistive component R is responsible for the damping. In an electric circuit
$$-c = \frac{1}{RC}$$ or $$-c = \frac{R}{L}$$ or a combination of those.

Last edited by a moderator: Jun 14, 2005