6.1WAVESWAVES

DAMPING AND RESONANCE

IN AN OSCILLATING SYSTEMS

LEARNING OUTCOMES

By the end of this lesson, the student shouldbe able to:

• Describe damping in an oscillating system

• Describe resonance in a oscillating system• Describe resonance in a oscillating system

• What can you say about the amplitude of theswing?

• What can you do to maintain or increase theamplitude?

• At the start, the pendulum oscillateswith maximum amplitude.

• The amplitude of the oscillationdecreases with time and finally stops.

What causes the pendulum to stop?

• Air friction causes the amplitude of thependulum to decrease.

• When the pendulum oscillates, it has energy.

• This energy is used to overcome air friction.

• As time passes, more energy of the pendulum• As time passes, more energy of the pendulumis being used to overcome air friction.

• This causes the energy of the pendulum todecreases.

• As a result, the amplitude becomes smaller.

• The pendulum is said to experience damping.

Damping

• Damping is the decrease in the amplitude ofan oscillating system when its energy is lostas heat energy.

• The amplitude of an oscillating system will• The amplitude of an oscillating system willgradually decrease and become zero whenthe oscillation stops.

Activity 2:Damping effect in a

vibrating system• Set up the apparatus as

shown below.• Fix a saw blade

horizontally on the leg ofa laboratory bench usinga laboratory bench usinga G-clamp.

• At the other end of theblade, fix a piece ofplasticine (50 g)

• Move the plasticine tothe position X andrelease it.

• Observe the position Yreached by the plasticine.

• Observe subsequent Ypositions of the plasticine.

Observation:What changes do youobserve in the positionY over severaloscillations?

Conclusion:

Position Y decreases

Conclusion:The position Y becomes _________ to theequilibrium position each time the plasticineoscillates.

closer

• Why does the spring oscillate closer and closer to theequilibrium position?

• Its amplitude decreases.

• What happens to the energy possessed by theplasticine and the blade?

• Energy possess decreases and lost to heat.

• What happens to the oscillation of the blade after a• What happens to the oscillation of the blade after along time?

• It will stop.

• What is the name given to this phenomenon?

• Damping

• How do you overcome the damping effect of theoscillation

• Give external force or push the plasticine ball.

• A mother puts herbaby to sleep in asarong cradle. Sheneeds tocontinuously movethe sarong cradle upand down.

What happen to the sarong cradlewhen the mother stops moving thecradle up and down?

• Amplitude decreases

Suggest a reason for themovement of the sarong cradlediscussed in (a).

• Damping, lost energy to heat• Damping, lost energy to heat

What must you do if you want tohelp the mother to maintain themovement of the cradle?

• Move the cradle up and down/ give external force

Forced oscillation & Damping

• The swing will stop • The boy is given a• The swing will stopswinging due todamping.

• The boy is given aperiodic push at thecorrect timing willcontinue to swingwithout stopping.

• A system oscillates atits natural frequencywhen no externalforce is applied to it.

• When a periodic force

• If a periodic force isapplied to the swingat its naturalfrequency, theamplitude of the

Forced oscillation & Damping

• When a periodic forceis applied to anoscillating system, theresponse depends onthe frequency of theperiodic force.

amplitude of theswing increases as theenergy of the swingincreases.

• The swing is said tobe in resonance and itoscillates with amaximum amplitude.

Resonance in an oscillating system

• To enable an oscillating system to go oncontinuously, an external force must beapplied to the system.

• The external force supplies energy to the• The external force supplies energy to thesystem. Such a motion is called a forcedoscillation

• Natural frequency is the frequency of asystem which oscillates freely without theaction of an external force.

Resonance in an oscillating system

Resonance occurs when a system is made tooscillate at a frequency equivalent to itsnatural frequency by an external force.natural frequency by an external force.

The resonating system oscillates at itsmaximum amplitude.

Barton’s pendulum

• The frequency of a simple pendulum dependson the length of the pendulum.

• In Barton’s pendulum experiment, there aremany pendulums tied to the rope. Two ofthe pendulum are of the same lengththe pendulum are of the same length

• When pendulum B oscillates, all the otherpendulums are forced tooscillate.

Barton’s pendulum

• But pendulum D oscillates with the largestamplitude, ie, pendulum D resonates

• Pendulum B and pendulum D are of the samelength.

• Frequency B equal Frequency D• Frequency B equal Frequency D

• Therefore, pendulum B causes pendulum Dto oscillate at its natural frequency.

Effects of resonance

• Breaking glass

The frequency of the sound is equal to thenatural frequency of the glass. Resonanceoccurs and the glass vibrates with largestamplitude and it breaks.amplitude and it breaks.

• Tacoma Bridge collapsed in 1940

The wind have the same frequency as thenatural frequency of the vibration of thebridge. Resonance occurred and caused thebridge to collapse.

Question 1

A system vibrates with a naturalfrequency. If a forced vibration of thesame frequency is given to the system,what will happen?what will happen?

A. Damping

B. Vibration

C. Resonance

• When does an oscillating systemexperiences damping?

A. When the amplitude of oscillationdecreases

Question 2

decreases

B when the period decreases

C when the frequency increases

D when the amplitude remainsconstant