$A$ particle executing simple harmonic motion of amplitude $5\, cm$ has a maximum speed of $31.4\, cm/s$. The frequency of its oscillation is ..... $Hz$.

The figure shows the $x-t$ plot of a particle executing one-dimensional simple harmonic motion. Determine the signs of the position,velocity,and acceleration variables of the particle at $t = 0.3 \; s$,$t = 1.2 \; s$,and $t = -1.2 \; s$.

The function $(\sin \omega t - \cos \omega t)$ represents

Write the difference between periodic motion and simple harmonic motion.

$A$ point particle of mass $0.1 \ kg$ is executing $S.H.M.$ with an amplitude of $0.1 \ m$. When the particle passes through the mean position,its kinetic energy is $8 \times 10^{-3} \ J$. Obtain the equation of motion of this particle if the initial phase of oscillation is $45^{\circ}$.

Equations $y = 2A \cos^2 \omega t$ and $y = A (\sin \omega t + \sqrt{3} \cos \omega t)$ represent the motion of two particles.