Problem 66E

An object is attached to the end of a vibrating spring and its displacement from its equilibrium position is y=8et/2sin4t, where t is measured in seconds and y is measured in centimeters. a Graph the displacement function together with the functions y=8et/2 and y=8et/2.How are these graphs related? Can you explain why? b Use the graph to estimate the maximum value of the displacement. Does it occur when the graph touches the graph of y=8et/2? c What is the velocity of the object when it first returns to its equilibrium position? d Use the graph to estimate the time after which the displacement is no more than 2 cm from equilibrium.

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