First slide

Simple hormonic motion

Question

The time period of a particle in simple harmonic motion is 8 second. At t =0, it is at the mean position. The ratio of the distances traveled by it in the first and second second is

Moderate

A

1 /2
B

1 $\sqrt{2}$
C

$1 / (\sqrt{2} - 1)$
D

$1 / \sqrt{3}$

Solution

$In S.H.M., y = asin ωt where ω = \frac{2 π}{T} = \frac{2 π}{8} = \frac{π}{4} At t = 1 \sec, y_{1} = asin (π / 4) = a / \sqrt{2} At t = 2 \sec, y_{2} = asin (π / 2) = a Now y_{2} - y_{1} = a - \frac{a}{\sqrt{2}} = \frac{(\sqrt{2} - 1) a}{\sqrt{2}} ∴ \frac{y_{1}}{y_{2} - y_{1}} = \frac{1}{(\sqrt{2} - 1)}$

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