The displacement of a particle on a vibrating string is given by the equations(t) = 9 +15sin(9πt)where s is measured in centimeters and t in seconds. Find the velocity of the particle after t seconds.

Explanation:

Given the displacement of a particle expressed as

s(t) = 9 + 15sin(9πt) where s is measured incm and time in secs.

velocity is the change in displacement of the particle with respect to time:

v(t) = d(s(t))/dt

v(t) = 0+15(9π)cos(9πt)

v(t) = 135πcos(9πt)

Hence the velocity of the particle after t seconds is expressed as 135πcos(9πt)

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