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Class 11 Physics Chapter 4 Motion In A Plane
4 Motion in a plane 4.1 Introduction 4.2 Scalars and vectors 4.3 Multiplication of vectors by real numbers 4.4 Addition and subtraction of vectors – graphical method 4.5 Resolution of vectors 4.6 Vector addition – analytical method 4.7 Motion in a plane 4.8 Motion in a plane with constant acceleration 4.9 Relative velocity in two dimensions 4.10 Projectile motion 4.11 Uniform circular motion
Class 11 Physics Chapter 5 Laws of motion
Section Name Topic Name 5 Laws of motion 5.1 Introduction 5.2 Aristotle’s fallacy 5.3 The law of inertia 5.4 Newton’s first law of motion 5.5 Newton’s second law of motion 5.6 Newton’s third law of motion 5.7 Conservation of momentum 5.8 Equilibrium of a particle 5.9 Common forces in mechanics 5.10 Circular motion 5.11 Solving problems in mechanics
Class 11 Physics Chapter 6 Work Energy and Power
Section Name Topic Name 6 Work Energy and power 6.1 Introduction 6.2 Notions of work and kinetic energy : The work-energy theorem 6.3 Work 6.4 Kinetic energy 6.5 Work done by a variable force 6.6 The work-energy theorem for a variable force 6.7 The concept of potential energy 6.8 The conservation of mechanical energy 6.9 The potential energy of a spring 6.10 Various forms of energy : the law of conservation of energy 6.11 Power 6.12 Collisions
Class 11 Physics Chapter 7 Rotation motion
Topics Introduction Centre of mass Motion of COM Linear Momentum of System of Particles Vector Product Angular velocity Torque & Angular Momentum Conservation of Angular Momentum Equilibrium of Rigid Body Centre of Gravity Moment of Inertia Theorem of perpendicular axis Theorem of parallel axis Moment of Inertia of Objects Kinematics of Rotational Motion about a Fixed Axis Dynamics of Rotational Motion about a Fixed Axis Angular Momentum In Case of Rotation about a Fixed Axis Rolling motion
Class 11 Physics Chapter 9 mechanics properties of solid
Section Name Topic Name 9 Mechanical Properties Of Solids 9.1 Introduction 9.2 Elastic behaviour of solids 9.3 Stress and strain 9.4 Hooke’s law 9.5 Stress-strain curve 9.6 Elastic moduli 9.7 Applications of elastic behaviour of materials
Class 11 Physics Chapter 11 Thermal Properties of matter
Section Name Topic Name 11 Thermal Properties of matter 11.1 Introduction 11.2 Temperature and heat 11.3 Measurement of temperature 11.4 Ideal-gas equation and absolute temperature 11.5 Thermal expansion 11.6 Specific heat capacity 11.7 Calorimetry 11.8 Change of state 11.9 Heat transfer 11.10 Newton’s law of cooling
Class 11 Physics Chapter 14 Oscillations
Section Name Topic Name 14 Oscillations 14.1 Introduction 14.2 Periodic and oscilatory motions 14.3 Simple harmonic motion 14.4 Simple harmonic motion and uniform circular motion 14.5 Velocity and acceleration in simple harmonic motion 14.6 Force law for simple harmonic motion 14.7 Energy in simple harmonic motion 14.8 Some systems executing Simple Harmonic Motion 14.9 Damped simple harmonic motion 14.10 Forced oscillations and resonance
Class 11th Physics Online Class For 100% Result
About Lesson

Simple Pendulum

A simple pendulum is defined as an object that has a small mass (pendulum bob), which is suspended from a wire or string having negligible mass.     

  • Whenthe pendulum bob is displaced it oscillates on a plane about the vertical line through the support.
  • Simple pendulum can be set into oscillatory motion by pulling it to one side of equilibrium position and then releasing it.
Class 11 Physics Chapter 14 Oscillations Notes and NCERT Solution. provide study material to excel in exam.

Problem:-A cylindrical piece of cork of density of base area A and height h floats in a liquid ofdensity ρl. The cork is depressed slightly and then released. Show that the corkoscillates up and down simple harmonically with a period

 T = 2 π√hρ/ρlg

where ρ is the density of cork. (Ignore damping due to viscosity of the liquid)


Base area of the cork = A

Height of the cork = h

Density of the liquid = ρ1

Density of the cork = ρ

In equilibrium:

Weight of the cork = Weight of the liquid displaced by the floating cork

Let the cork be depressed slightly by x. As a result, some extra water of a certain volume is displaced. Hence, an extra up-thrust acts upward and provides the restoring force to the cork.

Up-thrust = Restoring force, F = Weight of the extra water displaced

F = ­–(Volume × Density × g)

Volume = Area × Distance through which the cork is depressed

Volume = Ax

∴ F = – A x ρ1 g …..(i)

According to the force law:

F = kx

k = F/x

where, k is constant

k = F/x = -Aρ1 g…. (ii)

The time period of the oscillations of the cork:

T = 2π√m/k      …. (iii)


m = Mass of the cork

= Volume of the cork × Density

= Base area of the cork × Height of the cork × Density of the cork

= Ahρ

Hence, the expression for the time period becomes:


           T = 2π√hρ/ρ1g


Damped SHM can be stated as:-

  1. Motion in which amplitude of the oscillating body reduces and eventually comes to its mean position.
  2. Dissipating forces cause damping.
  3. Consider a pendulum which is oscillating
  4. After some time we can observe that its displacement starts decreasing and finally it comes to rest.
  5. This implies that there is some resistive force which opposes the motion of the pendulum. This type of SHM is known as Damped SHM.

Damping Force:-

  • It opposes the motion of thebody.
  • Magnitude of damping force is proportional to the velocity of the body.
  • It actsin the opposite direction of the velocity.
  • Denoted by Fdwhere d is the damping force.
    • Fd= -b v where b is a damping constant and it depends on characteristics of the medium (viscosity, for example) and the size and shape of the block.
  • (-ive) directed opposite to velocity

Equation for Damped oscillations: Consider a pendulum which is oscillating.

It will experience two forces

  1. Restoring force Fs = -k x
  2. Damping Force Fd = -b v

The total force Ftotal =  F+ Fd       = -k x – b v

Let a (t) = acceleration of the block

Ftotal= m a (t)

-k x – b v = md2x/dt2

md2x/dt2 + kx + bv =0

or md2x/dt2 + b dx/dt+ kx=0   (v=dx/dt) (differential equation)

d2x/dt2+ (b/m) dx/dt+ (k/m) x=0  

After solving this equation

x(t) = A e–b t/2m cos (ω′t + φ ) (Equation of damped oscillations)

Damping is caused by the term e–b t/2m

  ω’ =angular frequency

Mathematically can be given as:-

   ω ′= −√ (k/m –b2/4m2)

Consider if b=0 (where b= damping force) then

x (t) = cos (ω′t + φ)( Equation of Simple Harmonic motion)

Graphically if we plot Damped Oscillations

Class 11 Physics Chapter 14 Oscillations Notes and NCERT Solution. provide study material to excel in exam.
Class 11 Physics Chapter 14 Oscillations Notes and NCERT Solution. provide study material to excel in exam.

In the above figure there are set of 5 pendulums of different lengths suspended from a common rope.

  • The figure has 4 pendulums and the strings to which pendulum bobs 1 and 4 are attached are of the same length and the others are of different lengths.
  • Once displaced, the energy from this pendulum gets transferred to other pendulums through the connecting rope and they start oscillating. The driving force is provided through the connecting rope and the frequency of this force is the same as that of pendulum 1.
  • Once pendulum 1 is displaced, pendulums 2, 3 and 5 initially start oscillating with their natural frequenciesand different amplitudes, but this motion is gradually damped and not sustained.
  • Their oscillation frequencies slowly change and later start oscillating with thefrequency of pendulum 1, i.e. the frequency ofdriving force but with different amplitudes.
  • They oscillate with small amplitudes. The oscillation frequency of pendulum 4 is different than pendulums 2, 3 and 5.
  • Pendulum 4 oscillates with the same frequency as that of pendulum 1 and its amplitude gradually picks up and becomes very large.
  • This happens due to the condition for resonance getting satisfied, i.e. the natural frequency of the system coincides with that of the driving force
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