Oscillations Flashcards
What happens when an object oscillates?
It moves back and forth about a fixed position
What is a free oscillation?
Where an object oscillates freely after an initial disturbance
Give an example of a free oscillator
A pendulum
What is a forced vibration/oscillation?
When an object is forced to vibrate by an external source
Give an example of a forced vibration/oscillation
Pushing a swing
What is amplitude? (In the context of oscillations)
The maximum displacement from the equilibrium position
What is frequency? (In the context of oscillations)
The number of oscillations per unit time
What is angular frequency?
The number of radians per unit time
What is the difference between angular velocity and angular frequency in oscillations?
Essentially no difference, except angular velocity is a vector, but angular frequency is a scalar
What are the conditions for simple harmonic motion?
There must be a mass that oscillates, an equilibrium position and a restoring force that returns the mass to its central position
Give examples of simple harmonic motion
A freely oscillating pendulum, molecules vibration in a sound wave
What is the definition of simple harmonic motion?
A body executes simple harmonic motion if its force is proportional to its displacement from the equilibrium position, and is directed towards that point
What does the graph of displacement against time for a freely oscillating pendulum look like?
A sin graph
What does the graph of velocity against time for a freely oscillating pendulum look like?
A cos graph
What does the graph of acceleration against time for a freely oscillating pendulum look like?
A -sin graph
What is meant by a damped system?
One where the amplitude decreases over time as energy is removed from the system due to friction.
Frequency and time period remain constant, and there is an exponential pattern as more energy is removed while the system moves faster
Give examples of a damped system
A pendulum, a trolley oscillating on springs, a mass on a spring in water
What is meant by critical damping?
Critical damping is where the object returns to the equilibrium position in the shortest possible time without any oscillation
Give examples of critically damped systems
An analogue meter, speedometer needle, modern elevators
What sort of damping is used in car suspension?
Damping that is just less than critical
What is meant by resonance?
A build up of large amplitude oscillation
When does resonance occur?
When the frequency of the external driving force matches the natural frequency of the system, and the energy is transferred to the system in the most efficient way
Outline an example of useful resonance
In microwave ovens. The external driving force is provided by the microwaves. The frequency of the microwaves matches the natural frequency of the water molecules which resonate and transfer energy to the food.
Outline an example where resonance is a problem
Resonance in structures due to wind (like bridges, such as Tacoma narrows?), in buildings (avoiding having buildings with the same natural frequency of minor tremors)
For a trolley and spring system, what do graphs for energy against displacement and energy against time look like?
Energy against displacement: elastic potential energy is a quadratic curve with a minimum at the origin, and kinetic energy is a negative quadratic with a maximum at x = 0
Energy against time: Kinetic energy is a cos graph and elastic potential energy is a sin curve (if assumed starting at 0 displacement and no friction)
Time period of this graph = 2 oscillations
Explain the shapes of the graphs for the relationship of amplitude against frequency of the external force for systems with and without damping
- The graph for the system without damping has a much sharper and higher peak which is also slightly to the right of the graph for the system with damping
- The natural frequency is lower with damping as the resultant force is lower therefore acceleration is lower (so time period and natural frequency decrease)
- Amplitude of vibrations decreases as more energy is removed from the system
- The y intercept of this graph tells us the amplitude of the external oscillator
