First slide

Simple hormonic motion

Question

The speed of a particle moving along a straight line, when it is at a distance (x) from a fixed point on the line is given by v²=108-9x²(in CGS unit), Then

Moderate

A

The motion is periodic but not simple hormonic
B

The motion is not periodic
C

The motion is simple harmonic with amplitude $2 \sqrt{3} cm$
D

The motion is simple harmonic with amplitude 3 cm

Solution

A particle executing SHM with angular frequency $ω$ and amplitude A has an instantaneous velocity $V = ω \sqrt{A^{2} - x^{2}}$ where x is the distance of the particle from a fixed point on its line of motion. The given equation can be reduced to the form, $V = 3 \sqrt{{(2 \sqrt{3})}^{2} - x^{2}}$ .(C.G.S unit)
Therefore the given equation represents SHM with amplitude $2 \sqrt{3} cm$

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