Question

The maximum velocity and acceleration of a particle in $\text{SHM}$ are $100\text{cm/s}$ and $157{\text{cm/s}}^2$ respectively. The time period in seconds will be :

• A. $4$
• B. $1.57$
• C. $0.25$
• D. $1$

Answer 1

The correct option is A $4$

In $\text{SHM}$,
Maximum velocity $v_{max}=A\omega =100\text{cm/s}$...........(1)
Maximum acceleration $a_{max}=A{\omega }^2=157{\text{cm/s}}^2$.......(2)
dividing eq.(1) to eq.(2), we get
$\omega =\frac{157}{100}=1.57\text{rad/s}$
Time period $\left(T\right)=\frac{2\pi }{\omega }$
$\Rightarrow T=\frac{2\times 3.14}{1.57}=4\text{s}$
Hence, option $\left(a\right)$ is the correct answer.