Topic 3 - Oscillations

Question 1

Oscillation

Answer 1

Continuously repeated movements

Question 2

Period (T)

Answer 2

The time taken for an object to complete one full oscillation

Question 3

Simple harmonic motion

Answer 3

The motion of an oscillating system.

There’s usually restoring force during the SHM, which tries to return the object to its Centre position

Question 4

Restoring force

Answer 4

F = -kx
Where the force is proportional to the distance from the center position and k is a constant that depends on the particular oscillating system

Question 5

Amplitude

Answer 5

The maximum displacement from the equilibrium position

Question 6

Period of a pendulum

Answer 6

T = 2π√l/g

Where L is the length of the pendulum string

Question 7

Angular velocity

Answer 7

• ω = θ/t
Where t is the time in seconds

• ω = 2πf

• ω = 2π/T
Where T is the period

Question 8

Horizontal distance

Answer 8

x = r cosθ

Question 9

Moving in a circle

Answer 9

x = r cos(ωt)

R can also be amplitude

Question 10

ω of a pendulum is √g/L

L is the length of the string of the pendulum

Answer 10

ω of a string is √k/m

K is the restoring force constant

Question 11

Acceleration acts in the opposite direction to the displacement

Answer 11

When displacement is zero so is the acceleration

And when X is max so is acc

Question 12

The displacement graph is a cosine graph

Answer 12

The acceleration graph is a negative cosine graph

The velocity is a negative sine graph

Question 13

During a swinging motion of a pendulum, at each end of the swing, it’s velocity is zero

Answer 13

So it has zero kinetic energy and a maximum potential energy at this point

Question 14

When the bob passes through the central position, it’s velocity is at a maximum

Answer 14

And the kinetic energy is at a maximum while the potential energy is at a minimum

Question 15

Free oscillation

Answer 15

A continuous exchange of PE and KE, caused by a restoring force which is proportional to the displacement.

Question 16

Natural frequency

Answer 16

The frequency at which the oscillating system naturally oscillates without external forces

Question 17

Forced oscillation

Answer 17

Forcing the the oscillating system to oscillate at another frequency than its natural one.
The frequency is called driving frequency

Question 18

Damped oscillations

Answer 18

These suffer a loss of energy in each oscillation reducing the amplitude over time

Question 19

Types of damping:

Answer 19

Under damping

Over damping

Critically damped (overshooting)

Question 20

Under damping

Answer 20

It’s when the oscillator completed several oscillations and the amplitude decreases exponentially
E.G. A normal pendulum

Question 21

Overdamping

Answer 21

The amplitude of the oscillation may drop so rapidly that the oscillator does not even complete one cycle
E.g. under water

Question 22

Critical damping or overshooting

Answer 22

When the oscillator returns to its equilibrium position in the quickest possible time without going past that position

Question 23

Undamped oscillation

Answer 23

Is when no energy is lost during oscillations

Question 24

Resonance

Answer 24

Is when a system is forced to vibrate at its natural frequency, absorbing more and more energy and thus increasing the amplitude.

Question 25

A simple setup of several pendulums can demonstrate resonance. They heavy swinging ball acts through the suspension wire to drive all the other pendulums at its natural frequency.

Answer 25

Only the pendulum with the same natural frequency will vibrate with a large amplitude. The pendulum has the same length of wire as the driving pendulum. The other pendulums show little movement because the driving frequency doesn’t match their natural frequency

Question 26

As the driving frequency applied to an oscillating system changes, it will pass through Natural frequencies of the system which causes large amplitude vibrations

Answer 26

The size of the vibrations at resonant frequencies can be so great that they damage the system