Chapter 13 - Oscillations

A pendulum moves repeatedly from one side to another. A mass attached to a spring moves around its equilibrium position. A vibrating tuning fork repeats its motion rapidly.

Oscillations Class 11 studies repeated motion and develops the important special case called simple harmonic motion.

Periodic and oscillatory motion

Periodic motion repeats after equal intervals of time.

Oscillatory motion is repeated to-and-fro motion around an equilibrium position.

Not every periodic motion is oscillatory, and not every oscillation is necessarily simple harmonic.

Students study:

• Time period

• Frequency

• Angular frequency

• Amplitude

• Phase

• Periodic functions

• Displacement as a function of time

Simple harmonic motion

Simple harmonic motion, or SHM, is an oscillation in which the restoring acceleration is directly proportional to displacement and directed towards the equilibrium position.

This condition may be written conceptually as:

Acceleration is opposite to displacement and proportional to it.

The equilibrium position is stable because the restoring force always acts towards it.

SHM and circular motion

SHM can be understood as the projection of uniform circular motion onto a diameter.

This relationship helps students understand the sinusoidal variation of displacement, velocity and acceleration.

Displacement, velocity and acceleration

During SHM:

• Displacement is measured from equilibrium

• Velocity is maximum at equilibrium

• Velocity is zero at extreme positions

• Acceleration is zero at equilibrium

• Acceleration magnitude is maximum at extreme positions

Students should understand these results physically rather than memorising a table.

Spring-mass system

For a mass attached to an ideal spring, the restoring force follows Hooke’s law.

Students study the force constant and derive the time period of oscillation.

The time period depends on mass and spring constant under the ideal model.

Energy in SHM

Energy changes continuously between kinetic and potential forms.

At equilibrium:

• Kinetic energy is maximum

• Potential energy is minimum

At the extreme positions:

• Kinetic energy is zero

• Potential energy is maximum

In ideal SHM, total mechanical energy remains constant.

Simple pendulum

A simple pendulum performs approximate SHM for small angular displacements.

Students derive its time period and study how it depends on length and gravitational acceleration.

The pendulum’s time period does not depend on the bob’s mass in the ideal model.

Common student mistakes

Students often:

• Treat every periodic motion as SHM

• Confuse frequency with angular frequency

• Measure displacement from an extreme instead of equilibrium

• Say acceleration is zero at an extreme position

• Assume speed is maximum at an extreme

• Apply the simple-pendulum result for large angles

• Confuse one complete oscillation with travel from one extreme to the other

How should you study Oscillations?

Begin with the meaning of equilibrium and restoring force. Then connect displacement, velocity and acceleration using graphs.

Use energy conservation to understand the motion instead of memorising isolated results.

Frequently Asked Questions

What is simple harmonic motion?

It is oscillatory motion in which restoring acceleration is proportional to displacement and directed towards equilibrium.

Is every periodic motion SHM?

No. SHM must satisfy the specific restoring-force condition.

Where is velocity maximum in SHM?

Velocity is maximum at the equilibrium position.

Where is acceleration maximum in SHM?

The magnitude of acceleration is maximum at the extreme positions.

Does a simple pendulum always perform SHM?

It performs approximate SHM only for small angular displacements.