5.3 Oscillations

Question 1

Spring oscillating definition for displacement

Answer 1

Displacement - distance from the equilibrium position (vector)

Question 2

Spring oscillating definition for Amplitude

Answer 2

Amplitude - maximum displacement

Question 3

Spring oscillating definition for period

Answer 3

Period - time taken for a complete oscillation

Question 4

Spring oscillating definition for Frequency

Answer 4

Frequency - number of oscillations per second

Question 5

State the equation relating angular frequency and

time period.

Answer 5

⍵ = 2π/T Where ⍵ = angular frequency, T = time period

Question 6

What are the conditions for SHM?

Answer 6

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

Question 7

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

Answer 7

1. A mass-spring system

2. A pendulum

Question 8

What is the constant of proportionality linking acceleration and displacement?

Answer 8

a = - ⍵2 x

Question 9

What is x as a function of t and ⍵?

Answer 9

x = Acos⍵t or x = Asin⍵t (where A is amplitude)

Question 10

Is velocity is maximum when displacement is maximum.

Answer 10

No, The velocity is minimum at the amplitude of oscillation, as the object changes direction. Velocity is maximum when the object passes through the equilibrium position.

Question 11

How can you calculate the maximum speed using ⍵ and A?

Answer 11

v max = ⍵A

Question 12

What is the difference between a displacement time graph and a velocity time graph

Answer 12

the velocity time graph is 1/4 of a wavelength ahead than the displacement time graph

Question 13

What is the difference between a displacement time graph and a acceleration time graph

Answer 13

The acceleration time graph is 1/2 a wavelength ahead of the displacement time graph

Question 14

graph for potential energy and kinetic energy against displacement for a SHM system.

Answer 14

At -A kinetic energy is at it’s at its lowest, potential energy is at it’s highest.
At the mid point between -A and +A the reverse is true kinetic at it’s highest and potential at it’s lowest.
At +A the kinetic energy is at it’s lowest and potential energy is at it’s highest

Question 15

What is damping?

Answer 15

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 16

explain the difference between

light damping, heavy damping and critical damping.

Answer 16

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 17

What is the difference between free and forced oscillations?

Answer 17

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 18

What is resonance?

Answer 18

When the driving frequency of the external force applied to 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 19

Describe an experimental technique to investigate the resonance of an object

Answer 19

● 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.