Question

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

• A. $20\pi s$
• B. $2\pi s$
• C. $\pi /5 \, s$
• 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 $\omega =\frac{2 \pi }{T}$
$\Rightarrow 16=\frac{1}{2}\times 5.12 \times \frac{4 \pi ^{2}}{\text{T}^{2}}\times 0.25^{2}$
$\Rightarrow T^{2}=\frac{2 . 56 \times 4 \pi ^{2} \times 0 . 25}{4}\times 0.25$
$\Rightarrow T=\frac{1 . 6 \times 2 \pi \times 0 . 25}{4}=\frac{\pi }{5}s$