What is the ratio of maximum acceleration to the maximum velocity of a simple harmonic oscillator?

$A$ particle of mass $250\,g$ executes a simple harmonic motion under a periodic force $F = (-25\,x)\,N$. The particle attains a maximum speed of $4\,m/s$ during its oscillation. The amplitude of the motion is $...........\,cm$.

The velocity of a particle executing simple harmonic motion along the $x$-axis is described by the equation $v^2 = 50 - x^2$,where $x$ represents displacement. If the time period of the motion is $\frac{x}{7} \ \text{s}$,the value of $x$ is . . . . . . .

$A$ particle is executing the motion $x = A \cos (\omega t - \theta)$. The maximum velocity of the particle is

$A$ particle in $SHM$ is described by the displacement equation $x(t) = A\cos(\omega t + \theta)$. If the initial $(t = 0)$ position of the particle is $1 \, cm$ and its initial velocity is $\pi \, cm/s$,what is its amplitude? The angular frequency of the particle is $\pi \, s^{-1}$.

$A$ body is performing simple harmonic motion with amplitude $A$ and time period $T$. The variation of its acceleration $(f)$ with time $(t)$ is shown in the figure. If at time $t$,the velocity of the body is $v$,which of the following graphs correctly represents the variation of velocity $(v)$ with time $(t)$?