Topic 13: Oscillations Flashcards
What are properties of an object moving in simple harmonic motion?
Simple harmonic motion is a specific type of oscillation where:
- Acceleration ∝ displacement
- Acceleration is in opposite direction to displacement
- a ∝ -𝑥
What is the force that causes simple harmonic motion?
Simple harmonic motion on an object is caused by a restoring force which acts towards the centre of equilibrium. e.g pendulum clocks
What sort of energy transfer occurs during SHM?
Kinetic energy transfers to potential energy; which type depends on system.
At amplitude, object has max potential energy.
As it moves towards equilibrium, PE transfers to KE.
Then when it starts to move away from equilibrium, KE transfers to PE.
What is the relation between the restoring force and the distance from equilibrium position?
- Restoring force is directly proportional to object’s distance from equilibrium position.
- F ∝ -𝑥
- F = -k𝑥
What is the amplitude of a object in SHM?
The amplitude of an object in SHM is the maximum displacement the object will move in SHM.
What is the time period of an object in SHM?
Time period of an object in SHM is the time taken for the object to return to initial position.
What formula is used for acceleration in SHM?
Acceleration of an object in SHM ∝ displacement in opposite direction; a ∝ -𝑥
a = -ω𝑥
Rearranging formula with ω=2πf:
a = -2πf𝑥
What are the 3 formulas of acceleration, velocity and displacement of an object in SHM?
𝑥 = A cosωt
v = -Aω sinωt
a = -Aω² cosωt
A - amplitude
t = time
ω = angular velocity
𝑥 - displacement
v - velocity
a - acceleration
Describe the system of a simple pendulum and the formula to work out Time period for it
A small, dense bob of mass 𝑚 hangs from a string with a length of 𝑙, which is attached to a fixed point.
T = 2π√𝑙/𝑔
Describe the system of a mass-spring system and formula to work out time period for it
A spring at a fixed point on a wall with a mass 𝑚 attached to it.
T = 2π√𝑚/𝑘
What are the assumptions of a mass-spring system?
Assumptions:
- no friction
- when stretched, mass moves to 0 displacement but carries on due to spring to negative displacement
- Spring compresses and no friction means object moves in SHM
What is resonance?
Resonance is where the driving force applied to an object causes amplitude to increase significantly.
How does resonance occur?
If the external driving force is equal to natural frequency of the object, resonance occurs. When it occurs, there is maximum energy transfer and max amplitude increases
What condition has to be met for resonance to occur?
Resonance only occurs when driving frequency of external force is equal to natural frequency of system.
How can resonance be dangerous?
For example, when people are crossing a bridge, they apply a driving force with frequency close to natural frequency. This could cause the bridge to oscillate violently which is dangerous and could damage bridge.
