First slide

Simple harmonic motion

Question

The total energy of a vibrating particle in S.H.M is E. If it’s amplitude and time period are doubled, it’s total energy will be

Moderate

A

16 E
B

8 E
C

4 E
D

E

Solution

$total energy of a vibrating particle E= \frac{1}{2} {mw}^{2} A^{2} E = \frac{1}{2} m {(\frac{2 π}{T})}^{2} A^{2} ---(1) n e w t i m e p e r i o d T^{1} = 2 T a n d a m p l i t u d e A^{1} = 2 A n e w e n e r g y of vibrating particle = E^{1} = \frac{1}{2} m {(\frac{2 π}{T^{1}})}^{2} {A^{1}}^{2} s u b s t i t u t e g i v e n v a l u e s E^{1} = \frac{1}{2} m {(\frac{2 π}{2 T})}^{2} {(2A)}^{2} E^{1} = \frac{1}{2} m {(\frac{2 π}{T})}^{2} A^{2} substitute eqn (1) E^{1} = E$

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