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

Answer 1

Answer: (A)

$\ce{ \sqrt{60} \times 0.2 \, m/s}$

Answer 2

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, $A = {20 \, cm = 0.2 \, m } ,k = 600 \, { N \, m^{-1}}$
$m = 10 {kg} , v_{\max} = ?$
$v_{\max} = 0.2 \sqrt{\frac{600}{10}} = 0.2 \sqrt{60} \, { m \, s^{-1} }$