Question

The dimensional formula for amplitude of $SHM$ is
(A) $MLT$
(B) ${M^0}{L^0}{T^0}$
(C) ${M^0}L{T^0}$
(D) $ML{T^0}$

Answer 1

Hint:The simple harmonic motion is a periodic motion in which the restoring force is equal to the object's displacement. The amplitude is the maximum displacement of the wave. The height of the peak point either on the crest or on the trough is calculated as the amplitude.

Complete step by step solution:
In the simple harmonic motion, the wave formed is periodic and has the equal crest and the trough region. So the amplitude is calculated either by finding the distance of the maximum point of the crest from the horizontal distance or by finding the distance of the maximum point of the trough from the horizontal axis. Since the amplitude is the

calculated distance, the unit of the distance is metre. The below diagram represents the amplitude of the wave.
Hence the unit of the amplitude must also metre. The dimension of the amplitude is calculated as follows.
Unit of amplitude $ = m$
Dimension of the amplitude $ = L$
Since the dimension of the amplitude does not contain any mass and the time parameters, the dimension of the amplitude is written as follows.
Dimension of the amplitude $ = {M^0}L{T^0}$ .

Thus the option (C) is correct.

Note:The part of the wave that is above the horizontal axis is considered as crest and the part of the wave which is below the horizontal axis is considered as the trough. In the answer, the mass and the time parameters are taken as the power of zero, because the value of anything power zero is one. So the one multiplied by anything is anything.