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Question:

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

y(t)=4sin(πt2), where y in m

y(t)=3cos(3πt2), where y in m

y(t)=3cos(πt2), where y in m

y(t)=-3cos2π, where y in m

Solution:

Correct option is C.
y(t)=3cos(πt2), where y in m
At t=0, y displacement is maximum, so equation will be cosine function.
T=4s ⇒ ω=2π/T=2π/4=π/2 rad/s
So, y=acosωt
y=3cos(π/2t)