The graphs in the figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graph best represents the relationship obtained when $y$ is the time?

$A$ particle executing $SHM$ of amplitude $a$ has a displacement of $-\frac{a}{2}$ at $t = \frac{T}{4}$ and a positive velocity. Find the initial phase of the particle.

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

The displacement of a particle varies according to the relation $x = 3 \sin 100t + 8 \cos^2 50t$. Which of the following is incorrect about this motion?

$A$ mass $m = 100 \, g$ is attached at the end of a light spring which oscillates on a frictionless horizontal table with an amplitude equal to $0.16 \, m$ and a time period equal to $2 \, s$. Initially,the mass is released from rest at $t = 0$ and displacement $x = -0.16 \, m$. The expression for the displacement of the mass at any time $t$ is:

If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \text{ m}$ represents the motion of a particle executing simple harmonic motion,the amplitude and time period of motion,respectively,are