The equation of motion of a particle is $x = a \cos(\alpha t)$. The motion is

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.

The equation of motion of a particle is $\frac{d^2y}{dt^2} + Ky = 0$,where $K$ is a positive constant. The time period of the motion is given by

Two particles are executing Simple Harmonic Motion ($S$.$H$.$M$.). The equations of their motion are $y_1 = 10 \sin \left( \omega t + \frac{\pi}{4} \right)$ and $y_2 = 25 \sin \left( \omega t + \frac{\sqrt{3} \pi}{4} \right)$. What is the ratio of their amplitudes?

What is the importance of periodic $\text{sine}$ and $\text{cosine}$ functions in physics?

The equation of a simple harmonic motion is $X = 0.34 \cos(3000t + 0.74)$,where $X$ and $t$ are in $mm$ and $sec$ respectively. The frequency of the motion is: