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The block in the figure oscillates sinusoidally between x = +a and x = %u2212a. The coordinate is x(t) = a cos(wt).

In the questions below, express the answers in terms of a and w show and explain your work.

(a) What is the time for one complete cycle, a -> -a -> a?

(b) Calculate the velocity v(t).

(d) Calculate the average speed (averaged over a complete cycle).

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