$A$ particle is executing simple harmonic motion in one-dimension. If the amplitude of oscillations is $0.2 \,cm$ and if its velocity at the mean position is $5 \,m/s$, then the angular frequency of the oscillation is

$A$ $1.00 \times 10^{-20} \, kg$ particle is vibrating with simple harmonic motion with a period of $1.00 \times 10^{-5} \, s$ and a maximum speed of $1.00 \times 10^3 \, m/s$. The maximum displacement of the particle is

The velocity at the mean position of a particle executing $S.H.M.$ is $v$. What is the velocity of the particle at a distance equal to half of the amplitude?

$A$ 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 $\pi \, s^{-1}$.

$A$ particle is performing simple harmonic motion. Which of the following statements are correct?
$(i)$ Its velocity-displacement graph is parabolic in nature.
$(ii)$ Its velocity-time graph is sinusoidal in nature.
$(iii)$ Its velocity-acceleration graph is elliptical in nature.

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