First slide

Simple harmonic motion

Question

The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $π$ results in the displacement of the particle along

Moderate

A

Straight line
B

Circle
C

Ellipse
D

Figure of eight

Solution

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

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