Question

A mass m = 8 kg is attached to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is 200 N/m. The mass m is then released and begins to undergo small oscillations. The maximum velocity of the mass will be $(g=10m/s^2)$

• A. 1 m/s
• B. 2 m/s
• C. 4 m/s
• D. 5 m/s

Answer 1

The correct option is B

2 m/s

Mean position will be at a position where kx = mg

or $x=\frac{mg}{k}=\frac{8\times 10}{200}=\frac{2}{5}m=0.4m$

This is also the amplitude of oscillation

i.e., A = 0.4 m

Now, $v_{max}=A\omega =A\sqrt{\frac{k}{m}}$

$=\left(0.4\right)\sqrt{\frac{200}{8}}=2m/s$