$A$ particle is executing $SHM$ about $y=0$ along the $y$-axis. Its position at an instant is given by $y = (7 \, m) \sin(\pi t)$. Its average velocity for the time interval $0$ to $0.5 \, s$ is ........... $m/s$.

Fill in the blanks:
$1.$ The ratio of displacement at any position and ....... remains constant for a particle executing $SHM$.
$2.$ The radius of the reference circle is equal to the .......... of the oscillator.
$3.$ Increase in phase per second of $SHO =$ ......... .
$4.$ $SHO$ covers ......... distance in one periodic time.

Average velocity of a particle executing $SHM$ in one complete vibration is

The equation of simple harmonic motion may not be expressed as (each term has its usual meaning):

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

The displacement of a particle in $SHM$ is given by $x = 5 \sin(\pi t)$,where $x$ is in $cm$. What is the time taken by the particle to travel from the mean position to the position of maximum displacement (in $, s$)?