5.3 Oscillations

Question 1

Displacement, x is…

Answer 1

the distance from the equilibrium position

Question 2

Amplitue, A is…

Answer 2

the maximum displacement

Question 3

Period, T is…

Answer 3

the time taken to complete one full oscillation

Question 4

Frequency, f is…

Answer 4

the number of oscillations per unit time

Question 5

Phase difference, ϕ is…

Answer 5

the fraction of an oscillation between the position of two
oscillating objects (given by Δ𝑡/𝑇 × 2𝜋)

Question 6

Angular frequency, ω

Answer 6

the rate of change of angular position (given by 2𝜋f)

Question 7

What is (SHC) Simple harmonic motion ?

Answer 7

is a type of oscillation, where the acceleration of the oscillator is directly proportional to the displacement from the equilibrium position, and acts towards the equilibrium position

Question 8

equation for acceleration

Answer 8

a = − 𝑥ω^2

Question 9

The direction of acceleration is always

Answer 9

towards the equilibrium position, in the opposite direction to the displacement.

Question 10

An oscillator in simple harmonic motion is…

Answer 10

an isochronous oscillation, so the period of the oscillation is independent of the amplitude.

Question 11

Techniques to investigate the period and frequency of simple harmonic motion

Answer 11

The frequency of the oscillator is equal to the reciprocal of the period. The period of the oscillator, and hence the frequency, can be determined by setting the oscillator (such as a pendulum or a mass on a spring) in to motion, and using a stopwatch to measure the time taken
for one oscillation.

In order to increase the accuracy of this measurement, the time for 10 oscillations to take place can be measured, and this time divided by 10 to find the period. An oscillator in simple harmonic motion is an isochronous oscillation, so the period of the oscillation is independent of the amplitude. A fiducial marker is used as the point to start and stop timings, and is normally placed at the equilibrium position.

Question 12

There are two equations which can be used to determine the displacement of a simple harmonic
oscillator.

Answer 12

𝑥 = 𝐴 sin (𝜔t)
𝑥 = 𝐴 cos (𝜔t)

The sine version of the equation is used if the oscillator begins at the equilibrium
position, and the cosine version is used if the oscillator begins at the amplitude position.

Question 13

The velocity of the oscillator at a given time can be determined by finding the gradient of the graph at that point. The maximum velocity occurs…., with the oscillator being stationary at the amplitude points. The maximum acceleration occurs…, and is 0 when….

Answer 13

at the equilibrium position
at the amplitude points
the oscillator is at equilibrium position.

Question 14

The velocity, v, of the oscillator is given using the equation

Answer 14

𝑣 = ±𝜔(𝐴^2 − 𝑥^2)^0.5

Question 15

What’s w (omega)?

Answer 15

𝜔 is the angular frequency of the oscillator

Question 16

During simple harmonic motion, energy is
exchanged between the…

Answer 16

kinetic and potential forms, but total energy is always conserved.

Question 17

The maximum kinetic energy occurs…

Answer 17

at the equilibrium point, where the velocity is at a maximum.

Question 18

The maximum potential energy occurs at…

Answer 18

the amplitude positions, where displacement is at a maximum.

Question 19

Define damping

Answer 19

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 20

There are 3 types of damping

Answer 20

light damping
heavy damping
very heavy damping

Question 21

When does light damping occurs?

Answer 21

Light damping occurs naturally (e.g. pendulum oscillating in air), and the amplitude decreases exponentially

Question 22

When does heavy damping occurs?

Answer 22

Heavy damping occurs (e.g. pendulum oscillating in water, or a bridge oscillations being stopped by oil at key points) the amplitude decreases dramatically.

Question 23

When does very heavy damping occurs?

Answer 23

In critical damping (e.g. pendulum oscillating in treacle) the object stops before one oscillation is completed.

Question 24

What is treacle ?

Answer 24

a substance thick like syrup

Question 25

What’s free oscillation?

Answer 25

When an object oscillates without any external forces being applied, it oscillates at its natural frequency. This is known as free oscillation.

Question 26

When does forced oscillation occurs?

Answer 26

Forced oscillation occurs when a periodic driving force is applied to an object, which causes it to oscillate at a particular frequency.

Question 27

When does resonance occur?

Answer 27

When the driving frequency of the external
force applied to an object is the same as the natural frequency of the object, resonance occurs.

Question 28

What evident distinguishable effect resonance has on an object, if no damping occurs?

Answer 28

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 i.e. a resonant bridge breaking down when the amplitude of its oscillations lateral or vertical is too great and causes the bridge to rupture.

Question 29

It’s the effect of resonance dependent on the type of damping a forced oscillation undergoes. True or False.

Answer 29

True

Question 30

As damping is increased, the
amplitude will

Answer 30

decrease at all frequencies.

Question 31

As damping is increased, the maximum amplitude occurs at

Answer 31

a lower frequency.

Question 32

Techniques to investigate resonance

Answer 32

To investigate the resonance of an object experimentally, a mass can be suspended between two springs attached to an oscillation generator.

A millimetre ruler can be placed parallel with the spring-mass system to record the amplitude.

The driver frequency of the generator is slowly increased from zero, so the mass will oscillate with increasing amplitude, reaching maximum amplitude when the driver frequency reaches the natural frequency of the system.

The amplitude of oscillation will then decrease again as frequency is increased further.

The spring mass system experiences damping from the air so 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.

Question 33

What’s the kinetic energy formula of a spring with a mass attached to it on one of its ends and fixed on a vertical wall in terms of extension x and Ep? And explain why?

Answer 33

Ek=0.5KA^2 - Ep or Ek=0.5k(A^2-x^2)

This is because A is the amplitude of the wave motion produced by the oscillating spring, a.k.a. the maximum extension it experiences. Hence the Ee will equal to Ep when x =A, and since Ep= total energy of the system, then the first formula above it’s like expressing Ek=Et - Ep and the second is a mere further manipulation of the first one.

Question 34

At any instant during circular motion, the object’s speed is …

Answer 34

directed tangential to the circular path and the force is perpendicular (at right angles) to the tangential speed.