A) \[\frac{{{d}^{2}}y}{d{{t}^{2}}}+{{\omega }^{2}}y=0\]
B) \[\frac{{{d}^{2}}y}{d{{t}^{2}}}+{{\omega }^{2}}{{y}^{2}}=0\]
C) \[\frac{{{d}^{2}}y}{d{{t}^{2}}}-{{\omega }^{2}}y=0\]
D) \[\frac{dy}{dt}+\omega y=0\]
Correct Answer: A
Solution :
For a particle executing SHM, restoring force (F) is given by \[F=ma=m\frac{dv}{dt}\] \[=m\frac{{{d}^{2}}y}{d{{t}^{2}}}=-ky\] \[\Rightarrow \] \[\frac{{{d}^{2}}y}{d{{t}^{2}}}+\frac{k}{m}y=0\] where\[\frac{k}{m}={{\omega }^{2}}\]is the characteristic angular frequency of the system. Hence, equation becomes \[\frac{{{d}^{2}}y}{d{{t}^{2}}}+{{\omega }^{2}}y=0\]
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