Edexcel A Level (IAL) Physics-5.23 Velocity–Time Graph for an Oscillator- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -5.23 Velocity–Time Graph for an Oscillator- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -5.23 Velocity–Time Graph for an Oscillator- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
Velocity–Time Graphs for an Object Oscillating in Simple Harmonic Motion
A velocity–time graph shows how the velocity of an oscillating object varies with time. For simple harmonic motion (SHM), this graph is sinusoidal and is phase-shifted relative to the displacement–time graph.
Shape of the Velocity–Time Graph
- The graph is a smooth sine wave.
- Velocity oscillates between \( +A\omega \) and \( -A\omega \).
- The motion is periodic with period \( T \).
The velocity in SHM is given by:
\( v = -A\omega \cos \omega t \)
Key Features on the Graph
- Maximum speed: occurs at the equilibrium position.
- Zero velocity: occurs at maximum displacement.
- Period \( T \): time between successive identical points on the graph.
Gradient of the Velocity–Time Graph
The gradient of a velocity–time graph gives the acceleration:
\( a = \dfrac{dv}{dt} \)
Therefore:
- Steep gradient → large acceleration.
- Zero gradient → zero acceleration.
- Positive gradient → acceleration in the positive direction.
- Negative gradient → acceleration in the negative direction.
Acceleration at Key Points
- At maximum velocity: gradient = 0 → acceleration = 0.
- At zero velocity: gradient is maximum → acceleration is maximum.
This is consistent with the SHM acceleration equation:
\( a = -\omega^2 x \)
Phase Relationship
- Velocity is \( 90^\circ \) out of phase with displacement.
- Acceleration is \( 90^\circ \) out of phase with velocity.
- Acceleration is \( 180^\circ \) out of phase with displacement.
Interpreting Direction of Acceleration
- Positive gradient → acceleration positive.
- Negative gradient → acceleration negative.
- Acceleration always acts towards equilibrium in SHM.
Common Exam Interpretation Points
- Acceleration is NOT proportional to velocity.
- Acceleration depends on the gradient, not the height of the graph.
- Maximum acceleration occurs when velocity is zero.
- Zero acceleration occurs when velocity is maximum.
Example (Easy)
At which point on a velocity–time graph is the acceleration zero?
▶️ Answer / Explanation
Acceleration is zero where the gradient of the velocity–time graph is zero, which occurs at maximum and minimum velocity.
Example (Medium)
How can you tell from a velocity–time graph when the acceleration is greatest?
▶️ Answer / Explanation
- The graph has the steepest gradient.
- This occurs when velocity is zero.
Example (Hard)
An object has maximum positive velocity. Describe its acceleration at this instant.
▶️ Answer / Explanation
- The gradient of the graph is zero.
- The acceleration is zero.
- The object is passing through equilibrium.