$A$ particle moving along the $X$-axis executes simple harmonic motion. The force acting on it is given by: (Where $A$ and $K$ are positive constants)

$A$ particle executes $SHM$ on a straight line path. The amplitude of oscillation is $2 \, cm$. When the displacement of the particle from the mean position is $1 \, cm$,the numerical value of the magnitude of acceleration is equal to the numerical value of the magnitude of velocity. The frequency of $SHM$ (in $s^{-1}$) is:

$A$ particle vibrating simple harmonically has an acceleration of $16 \ cm/s^2$ when it is at a distance of $4 \ cm$ from the mean position. Its time period is: (in $s$)

For a particle executing simple harmonic motion, the displacement-time $(x-t)$ graph is as shown in the figure. The acceleration of the particle at $t=\frac{4}{3} \,s$ is

$A$ small wooden cube is placed on a plank. The plank performs a vertical $S$.$H$.$M$. of frequency $\frac{3}{\pi} \text{ Hz}$. The maximum amplitude of the plank so that the wooden block does not leave the plank is [take $g = 10 \text{ m/s}^2$].

Give the formula of force acting on a particle executing simple harmonic motion.