First slide

Simple hormonic motion

Question

The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure. y -projection of the radius vector of rotating particle P is

Moderate

A

$y (t) = 3 \cos (\frac{πt}{2}), where y in m$
B

$y (t) = - 3 \cos 2 πt, where y in m$
C

$y (t) = 4 \sin (\frac{πt}{2}), where y in m$
D

$y (t) = 3 \cos (\frac{3 πt}{2}), where y in m$

Solution

$Here T = 4 s, A = 3 m Time period T = \frac{2 π}{ω} \Rightarrow 4 = \frac{2 π}{ω} \Rightarrow ω = \frac{π}{2} When the time is noted from the extreme position, then y = Acos (ωt) \Rightarrow y = 3 \cos (\frac{π}{2} t)$

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