Question

The total energy of a vibrating particle in SHM is $E$. If its amplitude and time period are doubled, its total energy will be :

• A. $16E$
• B. $8E$
• C. $4E$
• D. $E$

Answer 1

The correct option is D $E$

The total energy of a vibrating particle in S.H.M is given by,

$E=\frac{1}{2}m{\omega }^2{a}^2$

$E=2{\pi }^{2}m(\frac{a}{T}{)}^2$ ($\omega =\frac{2\pi }{T}$)

Now, when time period and amplitude are double,

$\frac{2a}{2T}=\frac{a}{T}$

The new total energy is ,

$E_1=2{\pi }^{2}m(\frac{2a}{2T}{)}^2$

$E^{\prime }=E$

The correct option is D.