A particle is performing a linear simple harmonic motion. If the acceleration an

Question

A particle is performing a linear simple harmonic motion. If the acceleration and the corresponding velocity of the particle are a and v respectively, which of the following graphs is correct?

Options:

Answer: Option A
:
C
If a particle performs SHM with angular frequency '

ω

' and amplitude 'A',then its displacement from mean position will be equal to

x = A s i n ω t

, if its initial phase is equal to zero.
Velocity will be equal to

v = \frac{d x}{d t} = A ω c o s ω t \to (1)

and acceleration will be

α = \frac{d v}{d t} = - A ω^{2} s i n (ω t) \to

(2)
From these equations,

c o s ω t = \frac{v}{A ω}, s i n ω t = \frac{α}{- A ω^{2}}

Squaring and adding,

\frac{v^{2}}{A^{2} ω^{2}} + \frac{α^{2}}{A^{2} ω^{4}} = 1

If v is taken on the y-axis and

α

on the x-axis, then it will be an ellipse

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