Question

The kinetic energy of a particle executing S.H.M. is $16J$ when it is at its mean position. If the amplitude of oscillations is $25cm$ , and the mass of the particle is $5.12kg$ , then the time period of the oscillation is

• A. $20\pi s$
• B. $2\pi s$
• C. $\pi /5s$
• D. $5\pi s$

Answer 1

Answer: (C)

When the particle is in its mean position, the kinetic energy will be maximum,
$K_{\text{max}}=\frac{1}{2}m{\omega }^2{a}^2$ and $\omega =\frac{2\pi }{T}$
$\Rightarrow 16=\frac{1}{2}\times 5.12\times \frac{4{\pi }^2}{{\text{T}}^2}\times 0.25^2$
$\Rightarrow T^2=\frac{2.56\times 4{\pi }^2\times 0.25}{4}\times 0.25$
$\Rightarrow T=\frac{1.6\times 2\pi \times 0.25}{4}=\frac{\pi }{5}s$