First slide

Simple harmonic motion

Question

A slider is oscillating in SHM on an frictionless track with an amplitude A. You slow it so that its amplitude becomes half. Then the total mechanical energy in terms of previous value is

Moderate

A

$\frac{1}{2}$
B

$\frac{1}{3}$
C

$\frac{1}{\sqrt{5}}$
D

$\frac{1}{4}$

Solution

Initial total energy $= \frac{1}{2} m ω^{2} A^{2}$ ; final total energy $= \frac{1}{2} m ω^{2} {(\frac{A}{2})}^{2}$ .
$∴$ Total mechanical energy becomes $\frac{1}{4}$ th
Executives simple harmonic motion is

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