$A$ particle is performing $S.H.M.$ starting from the extreme position. The graphical representation shows that between displacement and acceleration,there is a phase difference of:

The maximum force acting on a particle executing simple harmonic motion is $10 \,N$. The force on the particle when it is midway between mean and extreme positions will be

The displacement versus time graph of $SHM$ is shown. Which of the following is its acceleration versus time graph?

$A$ horizontal platform with a small object placed on it executes a linear $S.H.M.$ in the vertical direction. The amplitude of oscillation is $40 \text{ cm}$. What should be the least period of these oscillations, so that the object is not detached from the platform (in $\pi \text{ s}$)? [Take $g = 10 \text{ m/s}^2$]

The displacement of an oscillating particle varies with time $t$ (in seconds) according to the equation $y (cm) = \sin \left[ \frac{\pi}{2} \left( \frac{t}{2} + \frac{1}{3} \right) \right]$. The maximum acceleration of the particle is approximately ..... $cm/s^2$.

Two simple harmonic motions of angular frequency $300 \ rad/s$ and $3000 \ rad/s$ have the same amplitude. The ratio of their maximum accelerations is