Oscillations Ques 1
1. 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 $\mathrm{P}$ is :
[2019]
(a) $y(\mathrm{t})=-3 \cos 2 \pi \mathrm{t}$, where $\mathrm{y}$ in $\mathrm{m}$
(b) $y(\mathrm{t})=4 \sin \left(\frac{\pi \mathrm{t}}{2}\right)$, where $\mathrm{y}$ in $\mathrm{m}$
(c) $y(\mathrm{t})=3\left(\frac{3 \pi \mathrm{t}}{2}\right)$, cos where $\mathrm{y}$ in $\mathrm{m}$
(d) $y(\mathrm{t})=3 \cos \left(\frac{\pi \mathrm{t}}{2}\right)$, where $\mathrm{y}$ in $\mathrm{m}$
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Answer:
Correct Answer: 1.(d)
Solution: (d) At $t=0$, $\mathrm{y}=3$, which is maximum displacement so equation will be cosine function.
$ \begin{aligned} & \omega=\frac{2 \pi}{T}=\frac{2 \pi}{4}=\frac{\pi}{2} \mathrm{rad} / \mathrm{s} \quad (\because T=4 \mathrm{s}) \\ & y=a \cos \omega t \Rightarrow y=3 \cos \frac{\pi}{2} t \end{aligned} $
BETA
