Physics

Problem

A vibrating string has vertical displacement (in centimeters) modeled by

s(t)=0.8\cos\bigl(12\pi t\bigr),

where

t

is time in seconds. Positive displacement indicates upward motion relative to the equilibrium position. (a) Determine the instantaneous velocity function

v(t)

of the string. (b) Calculate the instantaneous velocity at

t=0.02\text{ s}

. State the units of your answer. (c) Find the smallest positive time

t>0

at which the string changes direction from moving upward to moving downward. Justify your answer by analyzing the sign of

v(t)

immediately before and after this time.

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