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Restoring Force, Damping Force, and Effective Spring Constant

!Here's the actual problem:

A) What is a restoring force?

B) What is a damping force?

C) What is an effective spring constant?

Solution This solution is FREE courtesy of BrainMass!

A) What is a restoring force?

The restoring force of a spring is the force exerted by the spring in a direction opposite to that of the displacement of the spring and tries to pull the spring back to the equilibrium position. This restoring force is proportional to the negative displacement from the equilibrium position of the spring.

F = -kx, where k is called the spring constant.

B) What is a damping force?

A pure spring force results in Simple Harmonic Motion, which is a constantly varying sinusoidal motion. To decrease the oscillation, we use dampers which produce Damping Forces which are proportional to the velocity (or time derivative of position). Fd = -d*v where v is the velocity or v = dx/dt.

For example, consider the suspension of your automobile, supporting the body mass. You have four springs. You also have four friction elements, variously called dampers or dash pots or shock absorbers which provide damping to smooth out vibrations.

C) What is an effective spring constant?

If a system is comprised of many springs in various arrangements, we define an "effective string constant" (ESC) to come up with a single number that corresponds to the effect of all these springs put together.

For example, consider two springs with spring constants k1 and k2.

If they are connected in series, ESC = k1 + k2
If they are connected in parallel, 1/ESC = 1/k1 + 1/k2