Question

A particle executing linear SHM has a maximum velocity of 40 cm/s and maximum acceleration of 50 cm/s2. Find its amplitude and period of oscillation.

Answer 1

Dear Student ,
Here in this case from the given data ,
$$\begin{gathered} v_{max}=\omega A=40cm/s \\ And{a}_{max}={\omega }^{2}A=50cm/s^2 \\ Now,Amplitude=A=\frac{{\left(\omega A\right)}^2}{{\omega }^{2}A}=\frac{{\left(40\right)}^2}{50}=32cm \\ TimeperiodT=\frac{2\pi }{\omega }=2\pi \times \frac{\omega A}{{\omega }^{2}A}=2\pi \times \frac{v_{max}}{a_{max}}=2\pi \times \frac{40}{50}=5·026s \end{gathered}$$
Regards