Question

The differential equation of a particle executing simple harmonic motion along $y$-axis is :

• 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. $\frac{d^{2} y}{d t^{2}}+\omega y=0$

Answer 1

Answer: (A)

For a particle executing SHM, restoring force $(F)$ is given by
$F=m a=m \frac{d v}{d t}=m \frac{d^{2} y}{d t^{2}}=-k y $
$\Rightarrow \frac{d^{2} y}{d t^{2}}+\frac{k}{m} y=0$
where $\frac{k}{m}=\omega^{2}$ is the characteristic angular frequency of the system.
Hence, equation becomes $\frac{d^{2} y}{d t^{2}}+\omega^{2} y=0$