Question

A $10\,kg$ collar is attached to a spring (spring constant $600\, N/m$), it slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by $20\,cm$ and released. What is the speed of the oscillation?

• A. $ \sqrt{60} \times 0.2 \, m/s$
• B. $ 60 \times 0.2 \, m/s$
• C. $ 60 \times 2 \, m/s$
• D. $ 6 \times 0.2 \, m/s$

Answer 1

Answer: (A)

Angular frequency of spring - block system is given by
$\omega = \sqrt{\frac{k}{m}}$
Maximum speed in oscillation
$v_{\max} = A \omega = \sqrt{\frac{k}{m}}$
Here, $A = 20 \, cm = 0.2 \, m ,k = 600 \, N \, m^{-1} $
$m = 10 kg , v_{\max} = ?$
$v_{\max} = 0.2 \sqrt{\frac{600}{10}} = 0.2 \sqrt{60} \, m \, s^{-1} $