First slide

Simple harmonic motion

Question

Graph of $v^{2} V s x^{2}$ for a particle executing SHM is

Moderate

A

Straight line with positive slope
B

Circle
C

Ellipse
D

Straight line with negative slope

Solution

$\begin{array}{l} v = ω \sqrt{A^{2} - x^{2}} \\ \Rightarrow v^{2} = ω^{2} A^{2} - ω^{2} x^{2} \\ Let v^{2} = Y and x^{2} = X \\ So, Y = ω^{2} A^{2} - ω^{2} X \end{array}$
This is of the form Y = mX + c (equation of a straight line), where $c = ω^{2} A^{2}$ and slope, $m = - ω^{2}$ .

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