First slide

Simple harmonic motion

Question

The displacement of two identical particles executing S.H.M are represented by equation $x_{1} = 4 \sin (10 t + π / 6) a n d x_{2} = 5 \cos (w t)$ . For what value of 'w' energy of both the particles is same.

Moderate

A

8
B

7
C

9
D

6

Solution

$total energy of simple harmonic oscillator E= \frac{1}{2} {mA}^{2} ω^{2} m i s m a s s; A i s a m p l i t u d e; ω i s a n g u l a r v e l o c i t y g i v e n E_{1} {=E}_{2} \frac{1}{2} m A_{1} {^{2} ω_{1}}^{2} = \frac{1}{2} m A_{2} {^{2} ω_{2}}^{2} \Rightarrow A_{1} ω_{1} = A_{2} ω_{2}; {by question A}_{1} {=4; w}_{1} {=10; A}_{2} =5 ; substitute them \Rightarrow {4x10=5 ω}_{2}^{2} \Rightarrow ω_{2} = 8 u n i t s .$

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