First slide

Simple hormonic motion

Question

Time period of a particle in SHM is 8 sec. At t: 0, it is at mean position. Ratio of the distances travelied by it in the first and second, seconds is:

Easy

A

$\frac{1}{2}$
B

$\frac{1}{\sqrt{2}}$
C

$\frac{1}{\sqrt{2} - 1}$
D

$\frac{1}{\sqrt{3}}$

Solution

$x = A \sin (\frac{2 π}{8} t) In first second, x_{1} = A \sin (\frac{2 π}{8} \times 1) = \frac{A}{\sqrt{2}} In second second, x_{2} = A - \frac{A}{\sqrt{2}} = A (\frac{\sqrt{2 - 1}}{\sqrt{2}}) \Rightarrow \frac{x_{1}}{x_{2}} = \frac{1}{\sqrt{2} - 1}$

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