Question

A $5 \,kg$ collar is attached to a spring of spring constant $500 \,N \,m^{-1}$. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by $10\, cm$ and released. The time period of oscillation is

• A. $\frac{\pi}{5} s$
• B. $\frac{\pi}{2} s$
• C. $\pi\,s$
• D. $2 \pi\, s$

Answer 1

Answer: (A)

Here, $m = 5 \,kg, k = 500 \,N m^{- 1}, A = 10\,cm = 0.1\, m$
Time period of oscillation is
$T = 2\pi\sqrt{\frac{m}{k}} $
$= 2\pi\sqrt{\frac{5\, kg}{500 \,N\,m^{-1}}} $
$= \frac{2\pi}{10} \,s $
$= \frac{\pi}{5}\, s$