Question

The displacement of a particle (in metre) from its mean position is given by the equation $y=0.2({\text{cos}}^2\frac{\pi t}{2}-{\text{sin}}^2\frac{\pi t}{2})$. The motion of the above particle is

• A. Not simple harmonic
• B. Simple harmonic with the period equal to that of a second’s pendulum.
• C. Simple harmonic with the period double that of a second’s pendulum
• D. Simple harmonic with amplitude 0.4 m

Answer 1

The correct option is B Simple harmonic with the period equal to that of a second’s pendulum.

$y=0.2({\text{cos}}^2\frac{\pi t}{2}-{\text{sin}}^2\frac{\pi t}{2})$
$y=0.2\text{cos}\pi t$
$\therefore \text{A}=0.2$, $\text{T}=\frac{2\pi }{\pi }=2s$