First slide

Simple hormonic motion

Question

The maximum displacement of an oscillating particle is 0.05m. If its time period is 1.57s
(i) What is the velocity at the mean position ? (ii) What is its acceleration at the extreme position ?

Moderate

A

0.2 ms^–1, 0.2ms^–2
B

0.8 ms^–1, 0.8ms^–2
C

0.2 ms^–1, 0.8ms^–2
D

0.8 ms^–1, 0.2ms^–2

Solution

Max. displacements = Amplitude
A = 0.05m ; T = 1.57sec
velocity at mean position
$\large {v_{\max }}\, = \,\omega A\, = \frac{{2\pi }}{T} \times A\, = \,2 \times \frac{{3.14}}{{1.57}} \times 0.05$
$\large = \,4 \times 0.05\, = \,0.2m/\sec$
Acceleration at extreme position
$\large a\, = \, - {\omega ^2}A$
[-ve sign only direction]
$\large a\, = \,{\left[ {\frac{{2\pi }}{T}} \right]^2} \times A\,\, = \,{\left[ {\frac{{2 \times 3.14}}{{1.57}}} \right]^2} \times 0.05$
$\large = \,16 \times 0.05\, = \,0.8m/{\sec ^2}$

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