Oscillations Class 11th Notes - Free NCERT Class 11 Physics Chapter 14 Notes - Download PDF

The chapter oscillations of NCERT Class 11 Physics deals with different periodic motions. In this chapter, we will learn about simple harmonic motion and its uniform motion. The NCERT Class 11 Physics chapter 14 notes provide an excellent brief overview of the chapter oscillations. The basic mathematical equations in the chapter are covered in the Class 11 Physics chapter 14 notes. Accurate and detailed information has been provided in the oscillations class 11 notes pdf download. Derivations have not been provided in the CBSE Class 11 Physics chapter 14 notes.

Also, students can refer,

• NCERT Solutions for Class 11 Physics Chapter 14 Oscillations
• NCERT Exemplar for Class 11 Physics Solutions Chapter 14 Oscillations

NCERT Class 11 Physics Chapter 14 Notes

• Periodic Motion

A motion that repeats itself after a fixed interval of time is called periodic motion. e.g., orbital motion of the Earth around the Sun, motion of seconds’ arm of a clock, motion undergone by a simple pendulum, etc.

• Oscillatory Motion

A periodic motion which undergoes a to and fro else back and forth about a fixed point, is known as oscillatory motion, e.g., motion shown by a simple pendulum, motion of a spring etc.

Note that all oscillatory motions are periodic motions but all periodic motion are not oscillatory motions. Thus, visa-versa is not true.

• Harmonic Oscillation

The oscillation that is expressed in terms of a single harmonic function, which are sine or cosine function, is harmonic oscillation.

• Simple Harmonic Motion

A Simple harmonic motion is such that it will move in accordance with to and fro along a straight line.Under restoring force magnitude is directly proportional to that of the displacement.

A SHM can be expressed in the following manner:

y = a sin ωt

or

y = a cos ωt

a = amplitude of oscillation.

• Non-harmonic Oscillation

A non-harmonic oscillation is the combination of at least two harmonic oscillations.

Non-harmonic Oscillation is expressed as:

y = a sin ωt + b sin 2ωt

• Terms Related to SHM

1. Time Period: Time taken by a body to complete one whole oscillation is known as time period. It is symbolized by T.

2. Frequency: The number of oscillations completed by the body in one second is frequency. It is symbolized by v.

SI unit = ‘Hertz’ or ‘second^-1

Frequency = 1 / Time period

3. Angular Frequency: The product of frequency and the factor 2π is called angular frequency. It is symbolized by ω.

Angular frequency (ω) = 2πv

SI unit = ‘Hertz’ or ‘second^-1.

4. Displacement: A physical quantity which changes uniformly with respect to time in a periodic motion is displacement. It is symbolized by y.

5. Amplitude: The maximum displacement in any direction with respect to mean position is called amplitude. It is symbolized by a.

6. Phase: A physical quantity which shows the position and direction of motion of an oscillating particle, is known as a phase. It is symbolized by φ.

SHM is defined as the projection of the uniform circular motion on a circle of any diameter as reference.

• Some Important Formulae of SHM

1. Displacement in SHM at any instant is shown as:

y = a sin ωt

or

y = a cos ωt , where a = amplitude and ω = angular frequency.

2. Velocity of a particle undergoing SHM at any instant is expressed as :

v = ω √(a² – y²)

When at mean position, y = 0 and v = maximum

v_max = aω

When at an extreme position, y = a and v=0.

3. Acceleration of a particle undergoing SHM at any instant is shown by

A or α = – ω² y

The acceleration is towards the mean position, and so the negative sign signifies the opposite to that of increase in displacement

At mean position y = 0 and acceleration = 0.

At extreme position y = a and acceleration = maximum

A_max = – aω²

4. Time period in SHM is shown by T = 2π √Displacement / Acceleration

• Graphical Representation

The acceleration is maximum when the velocity is minimum and vice versa.

Incase a particle undergoing SHM the phase difference between

(i) Instantaneous displacement and Instantaneous velocity

= (π / 2)ͨ

(ii) Instantaneous velocity and Instantaneous acceleration

= (π / 2)ͨ

(iii) Instantaneous acceleration and Instantaneous displacement

= πͨ

The graph of velocity versus displacement for a particle executing SHM is elliptical.

• Force in SHM

Acceleration of body in SHM is α = -ω² x

Applying the equation of motion F = ma,

F = – mω² x = -kx

Where, ω = √k / m and k = mω2 and ‘k’ constant and sometimes it is called the elastic constant.

The force is proportional and opposite to the displacement ( in SHM).

• Energy in SHM

The Kinetic energy of a particle is K = 1 / 2 mω² (A² – x²)

From above expression we can see that, the kinetic energy is maximum at centre (x = 0) and 0 at the extremes of the oscillation (that is x ± A).

The Potential energy of the particle, U =mω² x²/2

Above expression says, the potential energy has a minimum value at the centre (x = 0) and increases as the particle approaches either extremes of the oscillation (that is x ± A).

Total energy is obtained by adding potential and kinetic energies. Thus,

E = K + U = [m² ω²(A² – x²) + mω²x²]/2= mω²A²/2

where A = amplitude

m = mass of particle executing SHM.

ω = angular frequency and

v = frequency

Changes that occur in kinetic and potential energies during oscillations.

The frequency of total energy of particles executing SHM equals zero as total energy in SHM remains constant at every position.

When a particle of mass m undergoes SHM with a constant angular frequency (I), then the time period of oscillation (T)

Simple Pendulum

A simple pendulum has a heavy point mass which is suspended through a rigid support with the help of an elastic inextensible string.

The time period of a simple pendulum is expressed as :

T = 2π √l / g

where l = effective length of pendulum and g = acceleration due to gravity.

• Vibrations of Loaded Spring

The restoring force acts on spring under the condition when spring is stretched or compressed through a small distance y.

Restoring force (F) = – ky; Here k = force constant of spring.

In equilibrium, mass m is suspended to a spring system.

mg = kl

This expression is also used for Hooke's law.

Time period of a loaded spring is expressed in terms as follows:

T = 2π √m / k

Let the two springs of force constants k₁ and k₂.

These two constants are connected in parallel to mass m.

1. Effective force constant will be therefore,

k = k₁ + k₂

(ii) Time period

T = 2π √m / (k₁ + k₂)

These two constants are connected in series to mass m.

(i) Effective force constant will be therefore,

1 / k = 1 / k₁ + 1 / k₂

(ii) Time period is expressed as follows: T = 2π √m(k₁ + k₂) / k₁k₂

• Free Oscillations

When a body that can oscillate about its mean position is displaced from the mean position and then released, yet it oscillates back about its mean position. These oscillations are known as free oscillations and the frequency of oscillations is known as natural frequency.

• Damped Oscillations

Oscillations with a decreasing amplitude with respect to time are known as damped oscillations.

The displacement of the damped oscillator at any given instant t is expressed by

x = x'e^{– bt / 2m} cos (ω’ t + φ)

where x'^{e– bt / 2m} is the amplitude of the oscillator which decreases continuously with respect to time t and ω’.

The mechanical energy E of the damped oscillator at any given instant t is expressed by

E = 1 / 2 kx’²e^{– bt / 2m}

• Un-damped Oscillations

Oscillations with respect to time having constant amplitude are called un-damped oscillations.

• Forced Oscillations

Forced oscillations are those in which external periodic force is applied but the frequency does not match the value of natural frequency.

• Resonant Oscillations

.In resonant oscillations the external force is being applied which have the higher value of frequency than natural frequency and this causes increase in amplitude of the oscillations a type of oscillation is resonant oscillations

Mechanical Properties of Fluid class 11th notes will help students for reviewing the chapter and gaining a sense of the main points presented.

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