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(C) Given that,the force acting on the particle is $F = -kx + F_0$. We can rewrite this as $F = -k(x - \frac{F_0}{k})$. Let $y = x - \frac{F_0}{k}$,th

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about $x = \frac{F_0}{k}$ with $\omega = \sqrt{\frac{k}{m}}$

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(C) Given that,the force acting on the particle is $F = -kx + F_0$. We can rewrite this as $F = -k(x - \frac{F_0}{k})$. Let $y = x - \frac{F_0}{k}$,then the force becomes $F = -ky$. This is the standard form of the restoring force for Simple Harmonic Motion $(SHM)$,where the mean position is defined by $F = 0$. Setting $F = 0$,we get $-k(x - \frac{F_0}{k}) = 0$,which implies $x = \frac{F_0}{k}$. Thus,the particle oscillates about the mean position $x = \frac{F_0}{k}$. Comparing $F = -ky$ with the standard $SHM$ equation $F = -m\omega^2 y$,we get $m\omega^2 = k$. Therefore,the angular frequency is $\omega = \sqrt{\frac{k}{m}}$.

$A$ particle of mass $m$ is under the influence of a force $F = (-kx + F_0) \text{ N}$. The particle,when disturbed,will oscillate

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