First slide

Simple harmonic motion

Question

Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be

Moderate

A

A circle
B

An ellipse
C

A straight line
D

A parabola

Solution

If $y_{1} = a_{1} sinω t$ and $y_{2} = a_{2} \sin (ω t + 0) = a_{2} sinω t$
$\Rightarrow \frac{y_{1}^{2}}{a_{1}^{2}} + \frac{y_{2}^{2}}{a_{2}^{2}} - \frac{2 y_{1} y_{2}}{a_{1} a_{2}} = 0 \Rightarrow y_{2} = \frac{a_{2}}{a_{1}} y_{1}$
This is the equation of straight line.

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