# Working with spring oscillations and friction.

Not what you're looking for? Search our solutions OR ask your own Custom question.

A block attached to a spring is acted on by a spring with spring constant k and a weak frictional force of constant magnitude f. The block is pulled a distance Xo from the equilibrium and released. It oscillates many times and eventually comes to rest.

a) Show that the decrease of amplitude is the same for each cycle of oscillation.

b) Find the number of cycles of n the mass oscillates before coming to rest. Answer- n=(1/4)((kXo/f)-1)

Â© BrainMass Inc. brainmass.com November 24, 2022, 11:32 am ad1c9bdddfhttps://brainmass.com/physics/work/4960

#### Solution Preview

The equation of motion, from F = ma, is

<br>m x'' = -k x + f

<br>with f changing sign to oppose the velocity with each swing.

<br>

<br>For a block starting from rest at ...

$2.49