13 - Oscillations Flashcards
What are the two conditions required for an object to oscillate with SHM?
- The restoring force is directly proportional to the displacement.
- The restoring force always acts towards the equilibrium position.
What is angular frequency?
Angular frequency is a measure of the rate of rotation of an object.
Give two equations for angular frequency.
Ω = 2π/T
Ω = 2πf
What are the two types of oscillations that an object can experience?
Free oscillations
Forced oscillations
What is the frequency of a freely oscillating object equal to?
Freely oscillating object will vibrate at their natural frequency.
What is resonance?
Resonance is where the amplitude of oscillations of an object drastically increase due to gaining an increased amount of energy from the driving force.
This occurs when the driving frequency equals the natural frequency of the object.
What can be said about an object undergoing resonance?
The object will be oscillating at its maximum amplitude and the rate of energy transfer is at a maximum.
What is damping?
Damping occurs when energy is lost from an oscillating system due to an external force acting on it.
Damping is the process by which energy is dissipated in an oscillating system, leading to a reduction in the amplitude of oscillations over time.
What are the three types of damping?
- Light Damping
- Critical Damping
- Heavy Damping
What is critical damping?
Critical damping is when the damping causes the object to return to the equilibrium position in the quickest time possible without oscillating.
State the equation for the total energy stored in a simple harmonic oscillator.
Energy stored = ½ kA^2
Where k is the spring constant, and A is the amplitude.
If the following graph shows displacement against time, what would the velocity-time graph look like?
If the following graph shows displacement against time, what would the acceleration-time graph look like?
What is the difference between free and forced oscillations?
When an object oscillates without any external forces being applied, it oscillates at its natural frequency.
This is known as free oscillation. Forced oscillation occurs when a periodic driving force is applied to an object, which causes it to oscillate at a particular frequency.
3 different types of how damping occurs
Viscous damping
Coulomb damping
Structural damping
What is viscous damping
Resistance from a fluid (like air or oil) that opposes the motion of the oscillating object. The damping force is proportional to the velocity of the object
What is coulomb damping
Friction between sliding surfaces, which remains nearly constant and depends on the characteristics of the surfaces
What is structural damping
Internal friction within the material itself, often due to microscopic movements within the material’s structure
Describe energy in simple harmonic motion
Energy is conserved
The energy changes from kinetic energy to potential energy
What are free vibrations
They are not affected by any external varying forces
E.g a child on a swing will oscillate at a frequency that depends on the strength of the gravity and the length of the swing
The swing is said to oscillate with natural frequency
What are forced vibrations
When a system is made to oscillate by an external periodic force
E.g a loudspeaker is made to oscillate by the oscillating electrical signal from an amplifier
Light damping vs heavy damping
Light damping - the oscillations take a long time to fade away
Heavy damping - causes the object to oscillate hardly at all
Explain resonance
All objects have their own natural frequency
If the driving frequency is the same as the natural frequency the amplitude of vibration increases
This is called resonance
Equation for spring constant of springs in series vs parallel
Series:
1/k1 + 1/k2 = 1/kt
Parallel
K1 + k2 = kt
Explain how the plastic deformation of ductile materials reduce the amplitude of oscillation.
The plastic deformation of a ductile material can be used to reduce the amplitude of oscillations, this happens because energy is used to deform the material, decreasing the kinetic energy of the system and so the amplitude of oscillations …
Use a climbing rope to explain how plastic deformation reduces the amplitude of oscillation
A climbing rope is different from a rescue rope or a bungee cord:
A climbing rope is designed to extend when loaded suddenly
The rope stretches to reduce the amplitude of the oscillation when a climber falls onto it
It provides critical damping by immediately stopping the climber from bouncing
Explain the resonance curve
When f < f0, the amplitude of oscillations increases
At the peak where f = f0, the amplitude is at its maximum. This is resonance
When f > f0, the amplitude of oscillations starts to decrease
The maximum amplitude of the oscillations occurs when the driving frequency is equal to the natural frequency of the oscillator
As the degree of damping is increased, how is the resonance graph altered
The amplitude of resonance vibrations decrease, meaning the peak of the curve lowers
The resonance peak broadens
The resonance peak moves slightly to the left of the natural frequency when heavily damped
Describe a free oscillation
An oscillation where there are only internal forces (and no external forces) acting and there is no energy input
A free vibration always oscillates at its resonant frequency
What is the driving force
In order to sustain oscillations in a simple harmonic system, a periodic force must be applied to replace the energy lost in damping
This periodic force does work against the resistive force responsible for decreasing the oscillations
It is sometimes known as an external driving force
What are forced oscillations
Oscillations acted on by a periodic external force where energy is given in order to sustain oscillations
Forced oscillations are made to oscillate at the same frequency as the oscillator creating the external, periodic driving force
For example, when a child is on a swing, they will be pushed at one end after each cycle in order to keep swinging and prevent air resistance from damping the oscillations
These extra pushes are the forced oscillations, without them, the child will eventually come to a stop
Describe the energy changes for an oscillation
At the amplitude of its oscillations the system will have the maximum amount of potential energy, as it moves towards the equilibrium position, this potential energy is converted to kinetic energy so that at the centre of its oscillations the kinetic energy is at a maximum, then as the system moves away from the equilibrium again, the kinetic energy is transferred to potential energy until it is at a maximum again and this process repeats for one full oscillation.
What is the combined effect of damping and plastic deformation on an oscillation
Both damping and plastic deformation work to dissipate energy from the oscillating system, leading to a gradual reduction in amplitude.
Damping converts kinetic energy into heat, while plastic deformation absorbs energy through permanent changes in the material’s structure
