A particle executes simple harmonic oscillation with an amplitude $a$. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:

Two simple Harmonic Motions of angular frequency $100 \mathrm{and} 1000 \mathrm{rad}/\mathrm{s}$ have the same displacement amplitude. The ratio of their maximum accelerations is$:$

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=\left(2\times {10}^{-2}\cos \pi t\right) \mathrm{m}$. The time at which the maximum speed first occurs is$:$