4.1 Oscillations

Question 1b

Marks: 2

The graph shows the displacement of an object with time.

(b)

On the graph, label the following:

(i)

the time period T

[1]

(ii)

the amplitude x₀

[1]

Key Concepts

Question 1c

Marks: 1

An object oscillates isochronously with a frequency of 0.4 Hz.

(c)

Calculate the period of the oscillation.

[1]

Key Concepts

Question 1d

Marks: 4

The graph shows the oscillations of two different waves.

4-1-1d-question-stem-sl-sq-easy-phy

(d)

For the two oscillations, state:

(i)

The phase difference in terms of wavelength λ, degrees and radians.

[3]

(ii)

Whether the oscillations are in phase or in anti-phase.

[1]

Key Concepts

Question 2a

Marks: 3

(a)

Fill in the blank spaces with a suitable word.

Objects in simple harmonic motion ____________ about an equilibrium point. The restoring force and ___________ always act toward the equilibrium, and are ____________ to ____________, but act in the opposite direction.

[3]

Key Concepts

Question 2b

Marks: 3

Hooke's law can be used to describe a mass-spring system performing simple harmonic oscillations. Hooke's Law states that;

F = −kx

(b)

State the definition of the following variables and an appropriate unit for each:

(i)

F

[1]

(ii)

k

[1]

(iii)

x

[1]

Key Concepts

Question 2c

Marks: 1

The graph shows the restoring force on a bungee cord.

4-1-2c-question-stem-sl-sq-easy-phy

(c)

Identify the quantity given by the gradient, where F = − kx

[1]

Key Concepts

Question 2d

Marks: 2

(d)

For an object in simple harmonic motion:

(i)

State the direction of the restoring force in relation to its displacement

[1]

(ii)

State the relationship between force and displacement

[1]

Key Concepts

Question 3a

Marks: 3

An object oscillates in simple harmonic motion. The graph shows the variation of displacement with time. The object starts from the equilibrium position when time t = 0.

4-1-3a-question-stem-sl-sq-easy-phy

(a)

For this object:

(i)

Describe the shape of the displacement-time graph

[1]

(ii)

Outline how the shape of the graph would change if the oscillation was measured from amplitude x₀

[2]

Key Concepts

Question 3b

Marks: 1

(b)

Identify the correct v-t graph for the oscillation of the object in the x-t graph from part (a)

[1]

Key Concepts

Question 3c

Marks: 1

(c)

Identify the correct a-t graph for the oscillation of the object in the x-t graph from part (a)

[1]

Key Concepts

Question 3d

Marks: 2

(d)

State the phase difference in radians between the displacement-time graph from part (a) and the correct velocity-time graph from part (b)

[2]

Key Concepts

Question 4a

Marks: 1

(a)

Define the term 'total energy' for a system oscillating in simple harmonic motion.

[1]

Key Concepts

Question 4b

Marks: 3

The graph shows the potential energy E_P, kinetic energy E_K and total energy E_T of a system in simple harmonic motion.

4-1-4b-question-stem-sl-sq-easy-phy

(b)

Add the following labels to the correct boxes on the graph:

E_T
E_P
E_K

[3]

Key Concepts

Question 4c

Marks: 4

The diagram indicates the positions of a simple pendulum in simple harmonic motion.

4-1-4c-question-stem-sl-sq-easy-phy

(c)

Identify the position of the pendulum when:

(i)

Kinetic energy is zero

[1]

(ii)

Potential energy is at a maximum

[1]

(iii)

Kinetic energy is at a maximum

[1]

(iv)

Potential energy is zero

[1]

Key Concepts

Question 4d

Marks: 2

The period of the oscillation shown in part (c) is 2.2 s.

(d)

Calculate the frequency of the oscillation

[2]

Key Concepts

Question 5a

Marks: 2

A mass-spring system oscillates with simple harmonic motion. The graph shows how the potential energy of the spring changes with displacement.

4-1-5a-question-stem-sl-sq-easy-phy

(a)

For the mass-spring system, determine:

(i)

The maximum potential energy

[1]

(ii)

The total energy

[1]

Key Concepts

Question 5b

Marks: 2

(b)

Using the graph in part (a), determine:

(i)

The amplitude x₀ of the oscillation

[1]

(ii)

The potential energy in the spring when the displacement x = 0.1 m

[1]

Key Concepts

Question 5c

Marks: 4

The block used in the same mass-spring system has a mass m of 25 g. The maximum kinetic energy of the block is 40 mJ.

(c)

Calculate the maximum velocity of the oscillating block

[4]

Key Concepts

Question 5d

Marks: 2

The spring constant k of the spring used is 1.8 N m⁻¹

(d)

Calculate the restoring force acting on the mass-spring system at amplitude x₀

[2]

Key Concepts