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Stiff Spring Motion

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Question: The displacement s cm of the end of a stiff spring at time t seconds is given by:
s = a (e^−kt) sin 2πft. Determine the velocity and acceleration of the end of the spring after 2 seconds if a = 3, k = 0.75 and f = 20.

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Solution Summary

For a given stiff spring displacement, velocity and acceleration are estimated in this solution.

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s = a (e^−kt) sin 2πft

velocity,
v = ds/dt = a * { e^(-kt) * cos(2pi f t) * 2pi f - k e^(-kt) * sin(2pi f t)} = a * e^(-kt) * {cos(2pi f t) * 2pi f - k * sin(2pi f t)}

acceleration,
A = dv/dt = a * [e^(-kt) * ...

Solution provided by:

Amrit Lal Ahuja, PhD (IP)

Education

BEng, Allahabad University, India
MSc , Pune University, India
PhD (IP), Pune University, India

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