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A block of mass m is attached to a massless spring having a spring constant k...

A block of mass m is attached to a massless spring having a spring constant k and moves on a horizontal surface. It oscillates along the x-axis about its equilibrium position at x = 0. There is a frictional force of constant magnitude f between the block and the surface. Suppose the mass is pulled to the right to x = A and released at time t=0.

(a) Find the position of the mass as it reaches the left turning point. Your answers should be expressed in terms of A, m, k and f. [One way to do this is to try a solution of the form x(t)=C+Dcos(wt).]

(b) Find the time it takes the mass to complete the first cycle.

(c) How much energy is lost to friction in this motion?

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