Question

A mass attached to a spring is displaced from its equilibrium position by 5cm and released. The system then oscillates in simple harmonic motion with a period of 1s. If that same mass–spring system is displaced from equilibrium by 10cm instead, what will its period be in this case?
A mass attached to a spring is displaced from its equilibrium position by and released. The system then oscillates in simple harmonic motion with a period of . If that same mass–spring system is displaced from equilibrium by instead, what will its period be in this case?

A) 0.5s
B) 2s
C) 1s
D) 1.4s

Answer 1

Answer:

C) 1 s

Explanation:

The period of a mass-spring system is given by the formula:

$T=2\pi \sqrt{\frac{m}{k}}$

where

m is the mass hanging on the spring

k is the spring constant

As we can see from the equation above, the period of the system does NOT depend on the initial amplitude of the oscillation. Therefore, even if the initial amplitude is changed from 5 cm to 10 cm, the period of the system will remain the same, 1 s.