Question

A spring block system oscillates simple harmonic motion in the vertical direction. If the time period of a system is T at the surface of the Earth then calculate the time period of a system at the surface of the Moon where gravitational acceleration is $\dfrac{1}{6}$ of the Earth:
A) $\dfrac{T}{6}$.
B) $\dfrac{T}{3}$.
C) $\dfrac{T}{{\sqrt 6 }}$.
D) $T$.
E) $T\sqrt 6$.

Answer 1

Simple harmonic motion is defined as the motion in which the restoring force on the oscillating body is always towards the equilibrium position of the body; also the body will only oscillate between the two extremes.

Formula used: The formula of the time period of the spring block system is given by,
$\Rightarrow T = 2\pi \sqrt {\dfrac{m}{k}}$
Where the time period is T, the mass of the body is m and the spring constant is k.

Complete step by step solution:
It is given in the problem that a spring block system oscillates simple harmonic motion in the vertical direction if the time period of a system is T at the surface of the Earth then we need to find time period of a system at the surface of the Moon where gravitational acceleration is $\dfrac{1}{6}$ of the Earth.
The formula of the time period of the spring block system is given by,
$\Rightarrow T = 2\pi \sqrt {\dfrac{m}{k}}$
Where the time period is T, the mass of the body is m and the spring constant is k.
Here we can observe that the time period of the oscillating body depends upon the mass and the spring constant and there is no term as acceleration due to gravity and therefore the time period of the spring block system does not depend upon the acceleration due to gravity.
So the time period of the spring block system on the moon is equal to T which means it means the same.

The correct answer for this problem is option D.

Note: The simple harmonic motion is a 1-d representation of a 2-d oscillating body. In this motion the restoring force always acts towards the equilibrium position of the body and the potential energy gets converted into kinetic energy and vice-versa. The time period depends upon the mass of the oscillating body and the spring constant.