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Oscillations — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsOscillations3 Marks
Question
A particle performing linear SHM has maximum velocity of $25 cm / s$ and maximum acceleration of $100 cm / s ^2$. Find the amplitude and period of oscillation, [ $\pi=3.142$ ]
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Answer

$ \text { Data : } v_{\max }=25 cm / s , a_{\max }=100 cm / s ^2$
$v_{\max }=\omega A \text { and } a_{\max }=\omega^2 A$
$\therefore \frac{a_{\max }}{v_{\max }}=\frac{\omega^2 A}{\omega A}=\omega \quad \therefore \omega=\frac{100}{25}=4 rad / s$
$\therefore \text { Amplitude, } A=\frac{v_{\max }}{\omega}=\frac{25}{4}=6.25 cm / s$
$\text { Period, } T=\frac{2 \pi}{\omega}=\frac{2 \pi}{4}=\frac{\pi}{2}=\frac{3.142}{2}=1.571 s$

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