Circular Motion and SHM

Question 1

What condition needs to be satisfied for an object moving in a circle?

Answer 1

There needs to be a force continuously acting at 90ᵒ to the object’s velocity and direction of motion.

Question 2

What are the two conditions for objects to undergo SHM?

Answer 2

Acceleration (and therefore force) must act in the opposite direction to displacement (from equilibrium).

Acceleration is proportional to displacement.

Question 3

What do the acceleration/time, velocity/time and displacement/time graphs look like for SHM?

Answer 3

If starting at amplitude:
- Acceleration:cos
- Velocity: -sin
- Displacement: -cos

If starting from 0, graphs shift 90ᵒ.

Question 4

What is damping?

Answer 4

• A damping force will resist the object’s motion and remove energy from the system.
• Light damping = amplitude decreases gradually (Energy ∝A²)
• Heavy damping = object won’t oscillate
• Critical damping = damping force is applied just as object reaches equilibrium, so it comes to a stop as quickly as possibe

Question 5

What is resonance?

Answer 5

• A driving force acts on a (lightly damped) system, adding energy and increasing the amplitude of the oscillations.
• The frequency of the driving force matches the natural frequency of the system (or a multiple of it).
• Driving force and restoring are 90ᵒ out of phase (driving force pushes most when object is at equilibrium).

Question 6

List the variables in the SHM speed equation.

Answer 6

• v: velocity
• ω: angular speed
• A: amplitude
• x: displacement

Question 7

Which direction does the resultant force on an object undergoing circular motion act?

Answer 7

Towards the centre of rotation.