First slide

Simple hormonic motion

Question

A particle is executing two different simple harmonic motions, mutually perpendiuclar, of different amplitudes and having phase difference of $\frac{π}{2}$ . The path of the particle will be

Difficult

A

circular
B

straight line
C

parabolic
D

Elliptical

Solution

$x = A \cos ω t a n d y = B \cos (ω t - \frac{π}{2}) = B \sin ω t$
$∴ {(\frac{x}{A})}^{2} + {(\frac{y}{B})}^{2} = 1 \Rightarrow Ellipse$

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