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### 4.1 Oscillations

"Oscillation is simply the to and fro motion about an equilibrium position."

What do I mean? Here's a simple illustration of oscillatory motion.

As explained in the video above, oscillatory motion takes place because a physical system is displaced from its equilibrium condition and are allowed to respond to the forces that tend to restore the equilibrium position. In addition to physical oscillation(which are usually termed as a mechanical oscillation) other non physical oscillation involve quantity such as magnetic field, electric field, current, voltage and so on.

Free oscillation occurs when a system is disturbed and the only force acting upon it is to restore the equilibrium position. Some examples of free oscillation are mass-spring system and a simple pendulum. However, we can also have an oscillations that is driven by some external force acting on it beside the already existing restoring force, such oscillation is termed as a forced oscillations.

Let us discuss the terms displacement, amplitude, period, frequency and angular frequency in context of oscillating system. Consider a graphs for any give physcal systems as below,

Displacement: The displacement is the difference between the value of the physical quantity and its equilibrium value.

Amplitude: The amplitude is the maximum magnitude of the displacement.

Period: The time taken for one complete oscillation is the period of the oscillation. Its denoted by $T$.

Frequency: The no of complete oscillations per unit time. Its SI unit is Hertz($Hz$) or $s^{-1}$.

Angular frequency: The angular frequency is the circular representation of frequency. The angular frequency ($\omega$) and the frequency $f$ are related by:
$$\omega = 2\pi f$$

Relation between the frequency and time period,
$$f\times T=1$$

$Ex.$ From the graph below,
1. Find displacement at t=0.8, t=1.475 and t=1.999
2. Find the Amplitude.
3. Find the Period and Frequency.
4. Find the Angular frequency.
graphing: desmos, references: universtiy physics