2019 OscillationsSimple Harmonic Motion and Uniform Circular Motion Medium Question 24 of 63 in Oscillations

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:

A $y(t)=-3\cos2\pi t$, where $y$ in m
B $y(t)=4\sin\left(\frac{\pi t}{2}\right)$, where $y$ in m
C $y(t)=3\cos\left(\frac{3\pi t}{2}\right)$, where $y$ in m
D $y(t)=3\cos\left(\frac{\pi t}{2}\right)$, where $y$ in m

The answer is D.

Solution


At $t=0$ the y-displacement is maximum, so the equation is a cosine function: $y=a\cos\omega t$
$\omega=\frac{2\pi}{T}=\frac{2\pi}{4}=\frac{\pi}{2}\ rad/s$, $a=3\ m$
$y(t)=3\cos\left(\frac{\pi t}{2}\right)$

Concept projection of circular motion

Oscillations in past papers

63 questions from this chapter have appeared across 26 exam years.