Edexcel A Level (IAL) Physics-5.19 Conditions for Simple Harmonic Motion- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -5.19 Conditions for Simple Harmonic Motion- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -5.19 Conditions for Simple Harmonic Motion- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
Condition for Simple Harmonic Motion and Identifying SHM
Simple harmonic motion (SHM) is a type of oscillatory motion in which a particle moves back and forth about a fixed equilibrium position under a restoring force.
Condition for Simple Harmonic Motion
A system undergoes simple harmonic motion if the restoring force acting on it is:
- Directly proportional to the displacement from equilibrium
- Always directed towards the equilibrium position
This condition is written mathematically as:
\( F = -kx \)
- \( F \) = restoring force (N)
- \( k \) = constant of proportionality (N m⁻¹)
- \( x \) = displacement from equilibrium (m)
- Negative sign indicates the force acts opposite to the displacement
Meaning of the Negative Sign
- If the object is displaced to the right, the force acts to the left.
- If the object is displaced to the left, the force acts to the right.
- The force always acts to restore the object to equilibrium.
Key idea: The restoring force always opposes the displacement.
Relation to Acceleration
Using Newton’s second law:
\( F = ma \)
Substitute \( F = -kx \):
\( ma = -kx \)
So:
\( a = -\dfrac{k}{m} x \)
Conclusion: In SHM, acceleration is directly proportional to displacement and opposite in direction.
Identifying Simple Harmonic Motion
To check whether a system performs SHM:
- Identify the equilibrium position.
- Determine the force (or acceleration) acting when the object is displaced.
- Check whether the force is proportional to displacement.
- Check whether the force is directed towards equilibrium.
If both conditions are satisfied, the motion is simple harmonic.
Common Examples of SHM
- Mass attached to a spring (within elastic limit)
- Small oscillations of a pendulum
- Object oscillating in a U-shaped tube
- Charge oscillations in an electrical oscillator (analogy)
Important: Not all oscillatory motion is SHM.
Situations That Are NOT SHM
- Large-angle pendulum oscillations
- Motion with constant restoring force
- Motion with friction or damping dominating
- Any motion where force is not proportional to displacement
Example (Easy)
Why does a mass on a spring execute simple harmonic motion?
▶️ Answer / Explanation
- The spring exerts a force proportional to extension.
- The force acts towards the equilibrium position.
- The condition \( F = -kx \) is satisfied.
Example (Medium)
An object experiences a force proportional to its displacement but acting away from equilibrium. Does it perform SHM?
▶️ Answer / Explanation
- The force does not act towards equilibrium.
- The negative sign condition is not satisfied.
- The motion is not SHM.
Example (Hard)
Explain why small-angle oscillations of a pendulum approximate to simple harmonic motion.
▶️ Answer / Explanation
- For small angles, restoring force is proportional to displacement.
- The force acts towards equilibrium.
- Thus the condition for SHM is approximately satisfied.