Question

The maximum displacement of the particle executing SHM is 1 cm and the maximum acceleration is ${(1.57)}^{2}cm\text{/}{s}^2.$ Its time period is

• A. 0.25 s
• B. 4.0 s
• C. 1.57 s
• D. 3.14 s

Answer 1

Answer: (B)

Maximum acceleration $=A{\omega }^2$ $\Rightarrow$ ${\left(\frac{\pi }{2}\right)}^2=1{\left(\frac{2\pi }{T}\right)}^2$ $\left(\because 1.57=\frac{\pi }{2}\right)$ $\Rightarrow$ $\frac{{\pi }^2}{4}=\frac{4{\pi }^2}{T^2}$ $\Rightarrow$ $T^2=\frac{4\times 4{\pi }^2}{{\pi }^2}$ $\Rightarrow$ $T^2=16$ $\Rightarrow$ $T=4s$