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Working with spring oscillations and friction.

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)

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>For a block starting from rest at ...