Question

If time period of SHM given by $X=Asin\omega t$ . then time period of motion given by $x=Asi{n}^2\omega tis?$

• A. T
• B. $\frac{T}{2}$
• C. 2T
• D. $\frac{T}{4}$

Answer 1

The correct option is B $\frac{T}{2}$

$\begin{array}{c}X=A\sin wt\\ T=\frac{2\pi }{w}\\ X=A{\sin }^{2}wt\\ =A\left(\frac{1-{\cos }^{2}wt}{2}\right)\\ T^{\prime }=\frac{2\pi }{2w}=\frac{T}{2}\\ Hence,\\ optionBiscorrectanswer.\end{array}$