Acceleration of a particle,executing $SHM$,at its mean position is

The acceleration $a$ of a particle undergoing $S.H.M.$ is shown in the figure. Which of the labelled points corresponds to the particle being at $-x_{max}$?

$A$ 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 ..... $cm/s^2$.

The graphs in the figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graph best represents the relationship obtained when $y$ is the unbalanced force acting on the system?

The magnitude of maximum acceleration is $\pi$ times that of maximum velocity of a simple harmonic oscillator. The time period of the oscillator in seconds is