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  4. A particle of mass 10 g is undergoing S.H.M. of amplitude 10 cm and period 0.1 s. The maximum value of force on particle is about

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Q. A particle of mass $10\, g$ is undergoing S.H.M. of amplitude $10 \,cm$ and period $0.1\, s$. The maximum value of force on particle is about

Oscillations

Solution:

$ T=0.1 \,\, m=0.01 \,kg$
$\therefore \omega =20\, \pi\, rad / s$
Amplitude $A=0.1 \,m$
$a=-\omega^{2} x$
Maximum acceleration $=-\omega^{2} A$
Maximum force $=-m \omega^{2} A$
$F_{\max } =-0.01 \times(20 \pi)^{2} \times 0.1$
$F_{\max } =-0.001 \times 400 \pi^{2}$
$=-3.95 \,N$
or $-4\, N$ approximately