Question

What is the formula for oscillation?

Answer 1

Periodic motion:

1. Periodic motion is defined as a sort of motion that repeats itself at regular periods of time.
2. Oscillatory or vibratory motion is the sort of motion in which an item travels to and fro or back and forth in a set interval of time about a fixed point.
3. The particle's net force is always oriented toward the equilibrium position.

The formula for oscillation:

1. The magnitude of the net force is always proportional to the particle's displacement from the equilibrium location at that time.
   Mathematically, $F_{\text{net}}=-kx$, where, $k$ is known as the force constant $\mathrm{ma}=-\mathrm{kx}$
   $a=-\frac{kx}{m}$ $\text{However,}a=-{\omega }^{2}x$, where,$\omega$ is known as the angular frequency
2. The time period of a particle executing S.H.M. refers to the time taken to complete one cycle. It is represented by $\mathrm{T}$. Mathematically,
   $T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}\left(\because \omega =\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}\right)$ , where $m$is the mass and $k$is the force constant.