These comprehensive RBSE Class 11 Physics Notes Chapter 14 Oscillations will give a brief overview of all the concepts.

→ Periodic motion: A motion which repeats itself over and over again after a regular internal of time is called a periodic motion.

→ Oscillatory motion: A motion in which a body moves to and fro repeatedly about a fixed point (called mean position) is called oscillatory or vibratory motion.

→ Time period:

It is the time taken by a particle to complete one oscillation about its mean position. It is denoted by T.

→ Amplitude:

The maximum displacement of the oscillating particle on either side of its mean position is called its amplitude.

→ Phase angle:

The phase of vibrating particle at any instant gives the state of the particle as regards its position and the direction of motion at that instant.

→ Periodic function:

Any function that repeats its value at regular intervals of its argument is called a periodic function.

→ Simple harmonic motion:

A particle is said to execute simple harmonic motion if it moves to and fro about a mean position under the action of a restoring force which is directly proportional to its displacement from the mean position and is always directed towards the mean position.

→ Restoring force:

A force which is directly proportional to its displacement from the mean position and it always tries to bring it back to mean position.

→ Simple pendulum:

A simple pendulum is a heavy point mass suspended by a weightless, inextensible and perfectly flexible string from a rigid support about which it can vibrate freely.

→ Free oscillations:

If a body, capable of oscillation is slightly displaced from its position of equilibrium and then released, it starts oscillating with a frequency of its own. Such oscillations are called free oscillations.

→ Damped oscillations:

The oscillations in which amplitude decreases gradually with the passage of time are called damped oscillations.

→ Forced oscillations:

When a body oscillates under the influence of an external periodic force, not with its own natural frequency but the frequency of the external periodic force, its oscillations are said to be forced oscillations.

→ Resonance:

It is a particular case of forced oscillations in which the frequency of the driving force is equal to the natural frequency of the oscillator itself and the amplitude of oscillations is greatest. Such oscillations are called resonance oscillations and the phenomenon is called resonance.

→ Frequency n = \(\frac{1}{T}\) or T = \(\frac{1}{n}\)

→ Simple periodic function

f(t) = Asinωt; g(t) = Acosωt

→ Restoring force in simple harmonic motion

F = -ky were k = mω_{0}^{2} = force constant

→ Differential equation of S.H.M.

\(\frac{d^2 y}{d t^2}\) + ω_{0}^{2}y = 0

Its solution, y = a sin (ω_{0}t + Φ)

→ Displacement equation of S.H.M.

y = aω_{0} cos ω_{0}t = aω_{0} cos \(\frac{2 \pi}{T}\)t

→ Velocity in S.H.M.

(i) v = aω_{0} cosω_{0}t = aω_{0} cos\(\frac{2 \pi}{T}\)t

(ii) v = ω_{0}\(\sqrt{a^2-y^2}\)

(iii) Relation between velocity and displacement 1

\(\frac{v^2}{\omega_0^2 a}+\frac{y^2}{a^2}\) = 1

→ Acceleration in S.H.M

f = -ω_{0}^{2}y = -aω_{0}^{2}sinω_{0}t = -aω_{0}^{2}sin \(\frac{2 \pi}{T}\)t

K = \(\frac{1}{2}\)k(a^{2} - y^{2})

Average kinetic energy, < K > = \(\frac{1}{4}\)ka^{2}

→ Potential energy in S.H.M.

(i) U = \(\frac{1}{2}\)ky = \(\frac{1}{2}\)k^{2} sin^{2} ω_{0}t

(ii) Average potential energy

< U > = \(\frac{1}{2}\)ka^{2}

→ Total energy in S.H.M

E_{total} = \(\frac{1}{2}\)kα^{2} = \(\frac{1}{2}\)mω_{0}^{2}α^{2} = 2π^{2} mn^{2}α^{2}

→ Time period of a body attached to a spring

T = 2π\(\sqrt{\frac{m}{K}}\)

→ Periodic time of simple pendulum

T = 2π\(\sqrt{\frac{l}{g}}\) or g = 4π^{2}\(\frac{l}{T^2}\)

→ Combination of springs in series

\(\frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}\) and T = 2π\(\sqrt{\frac{m\left(k_1+k_2\right)}{k_1 k_2}}\)

→ Parallel and other combination of springs

k = k_{1} + k_{2} and T = 2π\(\sqrt{\frac{m}{k_1+k_2}}\)

→ Damped force

F_{d} = -bv where b = damping constant

→ Periodic motion:

A motion which repeats itself over and over again after a regular interval of time.

→ Oscillation or cycle:

One complete to and fro motion of a particle.

→ Frequency:

It is the number of oscillations completed per second by a particle about its mean position.

→ Initial phase:

The phase of a vibrating particle corresponds to time t = 0 is called initial phase.

→ Second pendulum:

A seconds pendulum is a pendulum whose time period is two seconds.

→ Resonance:

A particular case of forced oscillations in which the frequency of the driving force is equal to the natural frequency of the oscillator itself and the amplitude of oscillations is greatest.

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