A) \[F=-k{{x}^{2}}-kv(t)\]
B) \[F=-kx-k{{d}^{2}}x/d{{t}^{2}}\]
C) \[F=-k{{x}^{2}}-kdx/dt\]
D) \[F=-kx-kdx/dt\]
Correct Answer: D
Solution :
: In case of free S.H.M. Acceleration\[\propto -\](displacement\[x\]) or force\[\propto -(m\times x)\] or \[{{F}_{1}}=-kx\] ... (i) Damping force\[\propto -\]velocity \[{{F}_{2}}\propto \frac{-dx}{dt}\] Or \[{{F}_{2}}=-k\left( \frac{dx}{dt} \right)\] ...(ii) From (i) and (ii), force\[={{F}_{1}}+{{F}_{2}}\] \[F=-kx-k\left( \frac{dx}{dt} \right)\]
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