First slide

Simple harmonic motion

Question

A body executing SHM at a displacement 'x' it’s PE is $E_{1}$ ,at a displacement ‘y’ its PE is $E_{2}$ . The PE at a displacement (x+y) is

Moderate

A

$\sqrt{E} = \sqrt{E_{1}} - \sqrt{E_{2}}$
B

$\sqrt{E} = \sqrt{E_{1}} + \sqrt{E_{2}}$
C

${E=E}_{1} {+E}_{2}$
D

${E=E}_{1} {-E}_{2}$

Solution

$P E o f a s i m p l e h a r m o n i c o s c i l l a t o r i s PE= \frac{1}{2} {mω}^{2} y^{2}, here m= mass, ω= angular velocity, y=displacement PE α y^{2} ⇒ \sqrt{P E} {α y, where mω}^{2} = c o n s \tan t y=k \sqrt{PE},here PE=E G i v e n a t d i s p l a c e m e n t x, P E = E_{1} ⇒ x=K \sqrt{E_{1}} ----(1) a t d i s p l a c e m e n t y, P E = E_{2} ⇒y=K \sqrt{E_{2}} ----(2) a t d i s p l a c e m e n t x + y, l e t P E b e E, \Rightarrow x+y=K \sqrt{E} ----(3) s u b s t i t u t e e q n 1, 2 i n 3 \Rightarrow K \sqrt{E_{1}} + K \sqrt{E_{2}} = K \sqrt{E} \sqrt{E} = \sqrt{E_{1}} + \sqrt{E_{2}}$

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