A charged particle of mass m and having a charge Q is placed in an electric field E which varies with time as $E=E_0\sin \omega t$. What is the amplitude of the S.H.M. executed by the particle?

$\begin{array}{l}\text{ For a particle undergoing SHM with an amplitude }A\text{ and }\\ \text{ angular frequency }\omega ,\text{ the maximum acceleration }={\omega }^2 \text{A}\\ \text{ Here the maximum force on the particle }={\text{QE}}_0\\ \therefore \text{ maximum acceleration }=\frac{{\text{QE}}_0}{ \text{m}}={\omega }^2 \text{A}\\ \Rightarrow \text{A}=\frac{{\text{QE}}_0}{ \text{m}{\omega }^2}\end{array}$