Question

A $5$ kg collar is attached to a spring of spring constant $500N{m}^{-1}$. 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)

$\frac{\pi }{5}$s

Here, $m=5kg,k=500N{m}^{-1},A=10cm=0.1m$
Time period of oscillation is

$T=2\pi \sqrt{\frac{m}{k}}=2\pi \sqrt{\frac{5kg}{500N{m}^{-1}}}=\frac{2\pi }{10}s=\frac{\pi }{5}s$