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  4. A particle of mass 250 g executes a simple harmonic motion under a periodic force F =(-25 x) N. The particle attains a maximum speed of 4 m / s during its oscillation. The amplitude of the motion is cm.

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Q. A particle of mass $250\, g$ executes a simple harmonic motion under a periodic force $F =(-25 x) N$. The particle attains a maximum speed of $4 \,m / s$ during its oscillation. The amplitude of the motion is __ $cm$.

JEE MainJEE Main 2023Oscillations

Solution:

$\frac{1}{4} a =-25 x ; a =-100 x $
$ \omega^2=100 \,\,\,\,\omega=10 $
$ \omega A =4 $
$ A =\frac{4}{10}=0.4 \,m $
$ A =40 \,cm $