# Oscillations Class 11 Notes Physics Chapter 14 - CBSE

## What Are Oscillations ?

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## Periodic Motion

A motion that repeats itself at regular intervals of time is called periodic motion.

## Time Period/frequency

The smallest interval of time after which the motion is repeated is called the 'period'. The number of oscillations/vibrations of motion is called frequency.

## Amplitude

The maximum displacement from mean position is called amplitude.

## Simple Harmonic Motion

•  Equation of SHM

x = A cos(wt + Φ)

x-displacement, A -amplitude (wt + Φ) – phase of the wave

w – angular frequency

Φ - phase constant

• Acceleration during oscillation is

α = – ω2y

• Velocity

$$v =\sqrt{\omega y_{0}^{2} - y^{2}}\\\text{V}_{max} = \omega y_{0}$$

• K.E. in S.H.M.

$$\text{K.E.} =\frac{1}{2}m\omega^{2}(y_{0}^{2} - y^{2})\\(\text{K.E.})_{max} =\frac{1}{2}m\omega^{2}y_{0}^{2}$$

• P.E. in S.H.M.

$$\text{P.E.} =\frac{1}{2}m\omega^{2}y^{2}\\\text{P.E}_{max} =\frac{1}{2}m\omega^{2}y_{0}^{2}$$

• Total energy in S.H.M.

$$\text{T.E.} =\frac{1}{2}m\omega^{2}y_{0}^{2}$$

## Time Period Of Various Systems

• Time period of simple pendulum

$$\text{T} =2\pi\sqrt{\bigg(\frac{l}{g}\bigg)}$$

(a) Effective restoring force in spring-mass system

F = – ky

$$\text{Time period, T} = 2\pi\sqrt{\bigg(\frac{m}{k}\bigg)}$$

(b) Two spring-one mass vertical system (series combination)

$$\text{Force constant =}\frac{k_{1}k_{2}}{k_{1} + k_{2}}\\\text{T} = 2\pi\frac{m(k_{1} + k_{2})}{k_{1}k_{2}}$$

(c) Two springs-one mass vertical system (Parallel combination)

k = k1+ k2+ k3

$$\text{T} =2\pi\frac{m}{(k_{1} + k_{2})}$$

(c) Two springs-one mass vertical system (Parallel combination)

k = k1 + k2 + k3

$$\text{T} = 2\pi\frac{m}{(k_{1} + k_{2})}$$

• Oscillations of a liquid column in a U-tube

$$\text{T} = 2\pi\sqrt{\bigg(\frac{h}{g}\bigg)}$$

• Oscillating of a floating object

$$\text{T} = 2\pi\sqrt{\bigg(\frac{\rho l}{dg}\bigg)}$$

• Oscillations of a pith-ball snug-fit in the neck of a bottle containing air

$$\text{T} =\frac{2\pi}{\text{A}}\sqrt{\bigg(\frac{mV}{\text{E}}\bigg)}$$

## Motion Of A Simple Pendulum In A Lift

• When the lift is either stationary or moving up or down with constant velocity

$$\text{T} = 2\pi\sqrt{\bigg(\frac{l}{g}\bigg)}$$

• When the lift is moving up with an acceleration a

$$\text{T = 2}\pi\sqrt{\bigg(\frac{l}{\text{g+a}}\bigg)}$$

• When the lift in moving down with an acceleration a < g

$$\text{T = 2}\pi\sqrt{\bigg(\frac{l}{g-a}\bigg)}$$

• When the lift is moving with an acceleration a = g then lift is having a free fall.