The block shown in the figure is acted on by a spring with spring constant \( k \) and a weak fr...

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The block shown in the figure 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 \( x_{0} \) from equilibrium position and then released. It oscillates many times and ultimately comes to rest.
(a) Show that the decrease of amplitude is the same for each cycle of oscillation.
(b) Find the number of cycles the mass oscillates before coming to rest.
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