First slide

Simple harmonic motion

Question

The motion of a particle varies with time according to the relation $y = \sqrt{2} \sin ω t + \sqrt{2} \cos ω t$ , then

Moderate

A

The motion is oscillatory but not S.H.M.
B

The motion is S.H.M. with amplitude $\sqrt{2}$
C

The motion is S.H.M. with amplitude 2
D

The motion is S.H.M. with amplitude 4

Solution

$R = \sqrt{a^{2} + b^{2} + 2 a b \cos ϕ}$
The given equation can be written as $y = a \sin ω t + b \sin (ω t + \frac{π}{2})$
$\begin{array}{l} Here ϕ = \frac{π}{2} \\ \begin{array}{l} R = \sqrt{a^{2} + b^{2} + (2 a b \cos \frac{π}{2})} \\ R = \sqrt{a^{2} + b^{2}} = \sqrt{a^{2} + a^{2}} = a \sqrt{2} \end{array} \end{array}$

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