• # question_answer The displacement of a particle (in metre) from its mean position is given by the equation $Y=0.2\,\,\,\left( {{\cos }^{2}}\frac{\pi t}{2}-{{\sin }^{2}}\frac{\pi t}{2} \right)$ A)  The motion of the above particle is not simple harmonicB)  Simple harmonic with the period equal to that of a second's pendulumC)  Simple harmonic with the period double that of a second's a pendulumD)  Simple harmonic with amplitude $0.4m$

Given that   $Y=0.2\,\left( {{\cos }^{2}}\frac{\pi t}{2}-{{\sin }^{2}}\frac{\pi t}{2} \right)$ $\Rightarrow$               $Y=0.2\,\cos \pi t$ This gives,   $A=0.2,$ $T=\frac{2\pi }{\pi }=2S$ (as $\omega =\pi$)