question_answer

The function \[R=\frac{{{R}_{1}}{{R}_{2}}}{({{R}_{1}}+{{R}_{2}})}\]represents

A)  a periodic, but not simple harmonic motion with a period \[R=\frac{{{R}_{1}}{{R}_{2}}}{({{R}_{2}}-{{R}_{1}})}\]

B)  a periodic, but not simple harmonic motion with a period \[{{\sin }^{2}}(\omega t)\]

C)  a simple harmonic motion with a period \[2\pi /\omega \]

D)  a simple harmonic motion with a period\[\pi /\omega \]

Correct Answer: B

Solution :

Here, \[\Rightarrow \] \[T=k{{C}^{x}}{{G}^{y}}{{h}^{z}}\] \[\Rightarrow \] For SHM.  \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{\text{0}}}{{\text{T}}^{\text{1}}}\text{ }\!\!]\!\!\text{ = }\!\![\!\!\text{ L}{{\text{T}}^{\text{-1}}}{{\text{ }\!\!]\!\!\text{ }}^{\text{x}}}{{\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{-1}}}{{\text{L}}^{\text{3}}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }}^{\text{y}}}{{\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }}^{\text{z}}}\] Hence, function is not SHM, but periodic. From the y-t graph, time period is \[\Rightarrow \]