First slide

Simple hormonic motion

Question

For a particle executing simple harmonic motion, determine the ratio of average acceleration of particle from extreme position to equilibrium position to the maximum acceleration.

Moderate

A

$\frac{4}{π}$
B

$\frac{2}{π}$
C

$\frac{1}{π}$
D

$\frac{1}{2 π}$

Solution

Let the equation of simple harmonic motion be,
$x = A \sin ωt$
Then, the required ratio is $\frac{\int_{0}^{\frac{T}{4}} ω^{2} A s i n ω t d t}{\frac{T}{4} \times ω^{2} A}$ = $\frac{2}{π}$

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