5.3 - Oscillations

Question 1

Angular frequency

Answer 1

A measure of an object’s angular displacement per unit time.

Question 2

Critical damping

Answer 2

The form of damping that reduces the displacement of an oscillating object to its equilibrium position in the quickest time possible and without further oscillation.

Question 3

Damping

Answer 3

The dissipation of energy from an oscillating system. The consequence is that the amplitude of oscillation will decrease. Damping occurs when a force opposes the system’s motion.

Question 4

Forced oscillations

Answer 4

Repeated up and down oscillations, at the frequency of a driver. The amplitude of oscillation is small at high frequencies and large at low frequencies.

Question 5

Free osicllations

Answer 5

Oscillations that are not caused by a driver. An object will naturally oscillate at its natural frequency.

Question 6

Isochronous oscillator

Answer 6

An oscillator whose frequency is independent to amplitude.

Question 7

Natural frequency

Answer 7

The frequency that a system naturally oscillates at when there is no driving force.

Question 8

Overdamping

Answer 8

A type of damping where the system is damped more than required to stop the oscillations. It takes longer for the system to return to equilibrium than for critical damping.

Question 9

Resonance

Answer 9

Resonance occurs when the frequency of oscillations is equal to the natural frequency of the oscillating system. The rate of energy transfer is at a maximum during resonance.

Question 10

Simple harmonic motion

Answer 10

Motion where the acceleration of an object is directly proportional, and in the opposite direction, to its displacement.

Question 11

Underdamping

Answer 11

A type of damping where energy is gradually removed from the system and the amplitude of oscillations slowly decreases.

Question 12

Displacement

Answer 12

Distance from the equilibrium position

Question 13

Amplitude

Answer 13

Maximum displacement

Question 14

Period

Answer 14

Time taken for a complete oscillation

Question 15

Frequency

Answer 15

Number of oscillations per second

Question 16

What are the conditions for SHM?

Answer 16

Acceleration must be directly proportional to displacement and in the opposite direction: a ∝ -x
It must act towards equilibrium

Question 17

What are the two main examples of systems which undergo SHM?

Answer 17

A mass-spring system
A pendulum

Question 18

What is the constant of proportionality linking acceleration and displacement?

Answer 18

-ω^2

Question 19

When is velocity a maximum?

Answer 19

When the object passes through equilibrium

Question 20

When is velocity a minimum?

Answer 20

At the amplitude of oscillation

Question 21

How can you calculate max speed?

Answer 21

Vmax = ωA

Question 22

Describe damping

Answer 22

Damping is the process by which the amplitude of the oscillations decreases over time.
This is due to energy loss to resistive forces such as drag or friction.

Question 23

Explain the differences between light damping, heavy damping and critical damping.

Answer 23

Light damping occurs naturally (e.g. pendulum oscillating in air), and the amplitude decreases exponentially (but time period remains constant as A and T are independent).
When heavy damping occurs (e.g. pendulum oscillating in water) the amplitude decreases dramatically.
In critical damping (e.g. pendulum oscillating in treacle) the object is stopped in as short a time as possible without overshooting equilibrium.

Question 24

What is the difference between free and forced oscillations?

Answer 24

When an object oscillates without any external forces being applied, it oscillates at its natural frequency. This is known as free oscillation.
Forced oscillation occurs when a periodic driving force is applied to an object, which causes it to oscillate at a particular frequency.

Question 25

What is resonance?

Answer 25

When the driving frequency of the external force applied to it an object is the same as the natural frequency of the object, resonance occurs. This is when the amplitude of oscillation rapidly increases, and if there is no damping, the amplitude will continue to increase until the system fails. As damping is increased, the amplitude will decrease at all frequencies, and the maximum amplitude occurs at a lower frequency.

Question 26

Describe an experimental technique to investigate the resonance of an object.

Answer 26

Suspend a mass between two springs attached to an oscillation generator and use a ruler parallel with the spring-mass system to record the amplitude. Increase the frequency of the generator slowly so that the amplitude increases, reaching maximum amplitude when the driver frequency is the same as the natural frequency of the system (after which, increasing the frequency will decrease the amplitude). Since drag force due to the air damps the system, the amplitude should not continue to increase until the point of system failure. To increase accuracy, the system can be filmed and the amplitude value recorded from video stills, as it can be difficult to determine this whilst the mass is oscillating.