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

$\begin{array}{l} E n e r g y o f a s i m p l e h a r m o n i c o s c i l l a t o r i s \\ E= \frac{1}{2} {mA}^{2} w^{2} \\ h e r e m = m a s s o f o s c i l l a t o r, A = a m p l i t u d e, w = a n g u l a r f r e q u e n c y \\ E_{1} {=E}_{2} \\ \Rightarrow m \frac{1}{2} {A^{2}}_{1} {w^{2}}_{1} = m \frac{1}{2} {A^{2}}_{2} {w^{2}}_{2} \\ \Rightarrow A_{1} ω_{1} = A_{2} ω_{2} \\ 10 \times 4 = 5 \times ω \\ ∴ ω = 8 r a d / s e c \end{array}$

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