On an average,a human heart is found to beat $75$ times in a minute. Calculate its frequency and period.

The motion of a particle executing simple harmonic motion is described by the displacement function,$x(t) = A \cos (\omega t + \phi)$. If the initial $(t = 0)$ position of the particle is $1 \; cm$ and its initial velocity is $\omega \; cm/s$,what are its amplitude and initial phase angle? The angular frequency of the particle is $\pi \; s^{-1}$. If instead of the cosine function,we choose the sine function to describe the $SHM$: $x = B \sin (\omega t + \alpha)$,what are the amplitude and initial phase of the particle with the above initial conditions?

$A$ particle is executing simple harmonic motion with an amplitude $A$. The distance travelled by the particle in half time period is

$A$ point particle of mass $200 \text{ g}$ is executing $S.H.M.$ of amplitude $0.2 \text{ m}$. When the particle passes through the mean position,its kinetic energy is $16 \times 10^{-3} \text{ J}$. The equation of motion of this particle is (Initial phase of oscillation $= 0^{\circ}$)

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 $t = -1.2 \; s$.

Identify the function which represents a periodic motion.