When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be :

Question

When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be : (A) Circular (B) Ellipitical (C) Sinusoidal (D) Straight line

Tardigrade Admin · Accepted Answer

For a particle in SHM, its speed depends on position as

v = ω A^{2} - x^{2}

Where

ω

is angular frequency and

A

is amplitude
Now

v^{2} = ω^{2} A^{2} - ω^{2} x^{2}

So,

\frac{v ^{2}}{( ω A ) ^{2}} + \frac{x ^{2}}{( A ) ^{2}} = 1

So graph between

v

and

x

is elliptical

Q. When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be :

Circular

Ellipitical

Sinusoidal

Straight line

For a particle in SHM, its speed depends on position as v=ωA2−x2​ Where ω is angular frequency and A is amplitude Now v2=ω2A2−ω2x2 So, (ωA)2v2​+(A)2x2​=1 So graph between v and x is elliptical

For a particle in SHM, its speed depends on position as
$v = ω A^{2} - x^{2}$
Where $ω$ is angular frequency and $A$ is amplitude
Now $v^{2} = ω^{2} A^{2} - ω^{2} x^{2}$
So, $\frac{v ^{2}}{( ω A ) ^{2}} + \frac{x ^{2}}{( A ) ^{2}} = 1$
So graph between $v$ and $x$ is elliptical