Question

1. A mass of 7 kg stretches a spring 0.21 m from its equilibrium position. The mass is removed and another body of mass 0.50 kg is suspended from its equilibrium the source spring. If the spring is now stretched and released, what is its period of motion?

Answer 1

Given:

$m_1=7\: kg$

$x_1=0.21 \:m$

$m_2=0.50\: kg$

$T-?$

The spring stiffness is equal

$$k=\frac{m_1g}{x_1}=\rm\frac{7\times 9.8}{0.21}=326.7\: N/m$$

The period of oscillation

$$T=2\pi\sqrt{\frac{m_2}{k}}=6.28\sqrt{\frac{0.50}{326.7}}=0.25\:\rm s$$