First slide

Simple hormonic motion

Question

The displacement of two identical particles executing SHM are represented by equations $\large {x_1}\, = \,4\sin \left( {10t + \frac{\pi }{2}} \right)\,\& \,{x_2}\, = \,5\cos \left( {\omega t} \right)$ . For what value of $\large \omega$ , energy of both the particles is same.

Easy

A

4 rad/s
B

8 rad/s
C

16 rad/s
D

32 rad/s

Solution

$\large E\, = \,\frac{1}{2}m{\omega ^2}{A^2}$
$\large {E_1}\, = \,{E_2}\, \Rightarrow \,\frac{1}{2} \times m \times {10^2} \times A_1^2\, = \,\frac{1}{2}m \times {\omega ^2} \times A_2^2$
$\large 100 \times A_1^2\, = \,{\omega ^2} \times A_2^2\,\, \Rightarrow \,100 \times 16\, = \,{\omega ^2} \times 25$
$\large {\omega ^2}\, = \,64\, \Rightarrow \,\omega \, = \,{\text{8 rad/sec}}$

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