Question

A particle performing linear simple harmonic motion has maximum velocity $25cm/s$ and maximum acceleration of $100cm/s^2$. Find the amplitude and period of oscillation. $(\pi =3.142)$

Answer 1

Given:-

${}_{V_{MAX}}=25cm/s^2$ $a_{max}=100cm/s^2$ $A=?$ and $T=?$

${}_{V_{MAX}}=\omega A$ and $a_{max}={\omega }^{2}A$ $\omega =\frac{a_{max}}{{}_{V_{MAX}}}=\frac{100}{25}=4$

$T=\frac{2\pi }{\omega }=\frac{44}{7\times 4}=\frac{11}{7}=1.57sec$

$A=\frac{{}_{V_{MAX}}}{\omega }=\frac{25}{4}=6.25cms$