Write the difference between oscillations and vibrations.

What is the value of frequency in the differential equation of $SHM$ $\frac{d^{2}x}{dt^{2}} + 100x = 0$?

Which of the following equations represents a simple harmonic motion? $(\omega$ is angular frequency, $A$ is amplitude of oscillation and $i = \sqrt{-1})$

$A$ particle moves on the $x-$axis according to the equation $x = x_0 \sin^2 \omega t$. Is the motion simple harmonic?

$A$ particle performs $SHM$ on the $x-$axis with a time period of $0.5 \, s,$ such that its velocity is zero at $x = -3 \, cm$ and at $x = 9 \, cm$. It was located at $x = 0$ and moving in the negative $x-$direction at $t = 0$. The equation of $SHM$ of the particle is:

$A$ particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small,which graph correctly depicts the position of the particle as a function of time $?$