Question

A particle executes linear harmonic motion about the point x-0. At t=0, it has displacement 8 mircrometerand zero velocity. If the frequency of the motion is 0.25 sec, determine (a) the period (b)the amplitude, (c) the maximum speed and (d) the maximum acceleration?
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Answer 1

Answer:

1. Time period = $\frac{1}{v}$ = $\frac{1}{0.25}$ = 4 s
2. Amplitude = 8 μm ( velocity is zero at max. and min. positions)
3. v(max) = Aω = 8 × $10^{-6}$ × 0.25 m/s = 2 × $10^{-6}$ m/s.
4. a(max) = Aω² = 8 × $10^{-6}$ × $(0.25)^{2}$ m/s² = 0.5 × $10^{-6}$ m/s²

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