Question

The maximum velocity and acceleration of a particle in S.H.M. are $100cms/sec$ and $157cm/se{c}^2$ 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

Maximum velocity by$V=\omega \sqrt{A^2-x^2}$

$V/max=\omega \sqrt{A^2-0}=A\omega$

acceleration $a=-{\omega }^{2}x$

$a/max=-{\omega }^{2}A$

value is $\left|a\right|={\omega }^{2}A$

ratio is $\frac{V_{max}}{\left|a\right|}=\frac{A\omega }{A{\omega }^2}=\frac{1}{\omega }$

So putties values $\frac{100cm/s}{157cm/s^2}=\frac{1}{\omega }$

$\Rightarrow \omega =1.57/sec$

Time period $T=\frac{2\pi }{\omega }=\frac{1.57\times 4}{1.57}=4sec$

$2\pi =2\times 3.14$

$=4\times 1.57$