11P14

Oscillations

Learning Objectives

• Periodic and Oscillatory Motion

• Simple Harmonic Motion (SHM) and Uniform Circular Motion

• Systems exhibiting SHM, Damped and Forced Oscillations

11P14.1

Periodic and Oscillatory Motions

11P14.1

CV 1

Periodic and Oscillatory Motions

Periodic Motion

Periodic Motion

Periodic Motion

Periodic Motion

• Motion that repeats itself after regular intervals of time.

Periodic Motion

Oscillatory Motion

• To and fro motion of an object about its mean position.

Periodic Motion

• Every oscillatory motion is periodic.
• But every periodic motion need not be oscillatory.

Periodic Motion

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11P14.1

CV 2

Period, Frequency and Displacement

Concept Test

Ready for a Challenge

17. A human heart beats at around 72 times in a minute. Calculate its frequency and period.

Pause the Video

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(Time Duration : 02 Minutes)

17. A human heart beats at around 72 times in a minute. Calculate its frequency and period.

Displacement

• Change in position under consideration with time.

Length

Angle

Concept Test

Ready for a Challenge

Pause the Video

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(Time Duration : 02 Minutes)

11P14.2

Simple Harmonic Motion and Uniform Circular Motion

11P14.2

CV 1

Simple Harmonic Motion (SHM)

Simple Harmonic Motion (SHM)

Motion along a straight line with an acceleration whose

• Direction is always towards a fixed point on the line and
• Magnitude is proportional to the distance from the fixed point

• Acceleration of the particle is directed towards a fixed point on the line.
• This fixed point (equilibrium position) is called the centre of oscillation.

• Magnitude of the acceleration is proportional to the displacement of the particle from this point.

Concept Test

Ready for a Challenge

Pause the Video

(Time Duration : 02 Minutes)

17. The resultant force acting on a particle executing simple harmonic motion is 20 N when it is 8 cm away from the centre of oscillation. Find the spring or force constant.

17. The resultant force acting on a particle executing simple harmonic motion is 20 N when it is 8 cm away from the centre of oscillation. Find the spring or force constant.

Spring Expands

Equilibrium Position

Spring at equilibrium position

Restoring Force

No

Equilibrium Position

Spring Compress

Equilibrium Position

Equilibrium Position

Spring Expand

Simple Harmonic Motion (SHM)

Spring Compress

Equilibrium Position

Spring Expand

• The maximum displacement on either side from the centre of oscillation is called the amplitude.

11P14.2

CV 2

Uniform Circular Motion

Uniform Circular Motion

• Uniform circular motion can be described as the motion of an object in a circle at a constant speed.

Uniform Circular Motion

Uniform Circular Motion

Concept Test

Ready for a Challenge

Pause the Video

(Time Duration : 02 Minutes)

11P14.2

CV 3

Velocity, Acceleration and Force in SHM

Simple Harmonic Motion (SHM)

Simple Harmonic Motion (SHM)

Direction of the acceleration is directed towards the centre of the circle.

Displacement, Velocity and Acceleration

Force is directed towards the mean position. Hence, also called restoring force.

{Newton’s Second

Law of Motion}

Concept Test

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Pause the Video

(Time Duration : 02 Minutes)

Concept Test

Ready for a Challenge

Pause the Video

(Time Duration : 02 Minutes)

11P14.2

CV 4

Energy in SHM

Energy in SHM

Energy in SHM

Total mechanical energy of the system

TE = PE + KE

Thus, total mechanical energy remains constant.

Energy in SHM

Spring normal

No Restoring Force

Equilibrium Position

Energy in SHM

As the particle is displaced away from the mean position

• KE decreases and PE increases.

Equilibrium Position

Concept Test

Ready for a Challenge

Pause the Video

(Time Duration : 02 Minutes)

11P14.3

Systems Exhibiting SHM, Damped and Forced Oscillations

11P14.3

CV 1

Oscillations due to Spring

Oscillations due to Spring

• Block attached to a spring fixed at one end.
• Block slides on a frictionless surface.
• Block once stretched, shows continuous motion about the mean position.

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Oscillations due to Spring

When the block is at mean position

• No restoring force acts.
• Spring is relaxed.

No Restoring Force

Equilibrium Position

Equilibrium Position

Restoring Force

Equilibrium Position

Restoring Force

Concept Test

Ready for a Challenge

Pause the Video

​

(Time Duration : 02 Minutes)

Equilibrium Position

11P14.3

CV 2

Oscillations due to Simple Pendulum

Oscillations due to Simple Pendulum

• Particle suspended from a fixed support through a light inextensible string.

m, g, L, I are constant for a given case

(Newton’s Law of rotational motion)

Let

Concept Test

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17. Calculate the time period of a simple pendulum of length one meter at moon.

Pause the Video

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(Time Duration : 02 Minutes)

17. Calculate the time period of a simple pendulum of length one meter at moon.

Concept Test

Ready for a Challenge

Pause the Video

​

(Time Duration : 02 Minutes)

17. What is the length of a simple pendulum, which ticks seconds?

17. What is the length of a simple pendulum, which ticks seconds?

11P14.3

CV 3

Damped Oscillations

Damped Oscillations

• Ideal (or free) oscillations continues forever.
• But in real life oscillations die out after some time. Eg – Swing.
• It is because an opposing force acts on it.
• Opposing force may be due to air drag, friction or any other resisting force.
• This opposing force is called damped force.
• The oscillations in which damped force acts are called Damped Oscillations.

Damped Oscillations

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Damped Oscillations

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Damped Oscillations

• Damping force depends on the nature of surrounding medium.
• Denser the surrounding medium, higher the magnitude of damping and the dissipation of energy is much faster.
• The damping force is generally proportional to velocity of the bob or block. [Stokes’ Law]
• It acts opposite to the direction of velocity.

Damped Oscillations

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Damped Oscillations

Equilibrium Position before the block is placed

Equilibrium Position after the block is placed

DE of motion of block under the influence of damping force

Damped Oscillations

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Decreases continuously with time

Decreases continuously with time

If the decrease is small

Concept Test

Ready for a Challenge

Pause the Video

​

(Time Duration : 02 Minutes)

>>>

Ignore

11P14.3

CV 4

Forced Oscillations and Resonance

Forced Oscillations

Oscillating system driven by a periodic force external to the oscillating system.

• Damping ceases the oscillations.

• If a force is applied that counters the damping force, then the oscillations are called Forced Oscillations.

When block is moving down

• Energy lost due to the damping force is compensated by the work done by the applied force.

Forced Oscillations

Forced Oscillations

• When the timing of push of swing exactly matches with the time period of swing, it gets the maximum amplitude.
• This amplitude is large, but not infinity, because there is always some damping in your swing.

Resonance

• Tacoma Narrows Bridge (1940 in US collapsed because the normal speed winds produced instability that matched the bridge's natural frequency.

Why are soldiers ordered to route step across a bridge?

Short answer is – RESONANCE !!

If they march in unison on the bridge, their marching frequency can match with the vibrational frequency of the bridge.

This will amplify the oscillation amplitude of the bridge.

It will cause the bridge to collapse.

Resonance