Answer to Question #226088 in Classical Mechanics for Cpha

Question

A 5.0-{\rm kg} block is suspended from the ceiling by a strong spring and released to perform simple harmonic motion with a period of 0.65 {\rm \;s} . The block is brought to rest, and the length of the spring with the block attached is measured. By how much is this length reduced when the block is removed?

Answer 1

The period of a spring pendulum is

$$T=2\pi\sqrt{\frac mk},\\\space\\ k=\frac{4\pi^2m}{T^2}=467.2\text{ N/m}.$$

According to equilibrium of forces:

$$mg=kx,\\\space\\x=\frac{mg}{k}=0.1049\text{ m}.$$