OCR A-Level Physics B H557
Planning
Implementing
Analysis
Evaluation
Practical Skills
Use of Apparatus and Techniques
Fundamental Data Analysis
Imaging and Signalling
Sensing
Mechanical Properties of Materials
Waves and Quantum Behaviour
Space, Time and Motion
Creating Models
Out Into Space
Our Place in the Universe
Matter: Very Simple
Matter: Hot or Cold
Electromagnetism
Charge and Field
Probing Deep Into Matter
Ionising Radiation and Risk
Creating Models
Solutions and graphs of simple harmonic motion
- 2 things to know
- Components 01, 02 and 03
Overview
Recall questions on the sine and cosine solutions of simple harmonic motion and when each applies, writing them with frequency, the displacement–time graph, the phase of velocity and acceleration against displacement, gradients linking the graphs, greatest speed at equilibrium, amplitude, angular frequency and maximum speed from x = 0.020 sin(30t), and spotting traces that are not simple harmonic.
What you need to know
Answer each one before you reveal it.
Which solution describes an oscillator released from maximum displacement at t = 0?
Questions from this subtopic
Each one with the model answer underneath.
- 1
What are the two standard solutions of the simple harmonic equation?
Model answer
The displacement is x = A sin(ωt) or x = A cos(ωt), depending on where the timing starts.
- 2
Which solution describes an oscillator released from maximum displacement at t = 0?
Model answer
The cosine solution x = A cos(ωt), because it gives x = A when t = 0.
- 3
Which solution describes an oscillator passing through equilibrium at t = 0?
Model answer
The sine solution x = A sin(ωt), because it gives x = 0 when t = 0.
- 4
Write the displacement equation in terms of frequency rather than angular frequency.
Model answer
The displacement is x = A sin(2πft) or x = A cos(2πft).
- 5
Describe the shape of the displacement–time graph of a simple harmonic oscillator.
Model answer
It is a sinusoidal curve of constant amplitude and constant period about the equilibrium position.
- 6
What is the phase relationship between displacement and velocity in simple harmonic motion?
Model answer
The velocity leads the displacement by a quarter of a cycle, that is by π/2 rad.
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