Waves; Topic 4.1 Oscillations Flashcards
What is the nature of an oscillation?
Oscillation motion is repetitive ie. periodic as it moves back and forth around an equilibrium position
Define amplitude
The maximum displacement from the equilibrium position
Define period
The time required to complete one cycle of a wave
What is the meaning of isochronous waves?
If the oscillations have a constant period, they are said to be isochronous
Define wavelength
the length of one complete oscillation measured from the same point on two consecutive waves
Define frequency of a wave
the number of oscillations per second and it is measured in hertz (Hz)
Simple harmonic motion (SHM) is defined as?
The motion of an object whose acceleration is directly proportional but opposite in direction to the object’s displacement from a central equilibrium position
An object is said to perform simple harmonic oscillations when all of the following apply:
The oscillations are isochronous
Amplitude and period are constant and independent of each other
There is a central equilibrium point
The object’s displacement, velocity and acceleration change continuously
There is a restoring force always directed towards the equilibrium point
The magnitude of the restoring force is proportional to the displacement
Define phase difference and how it is measured?
The phase difference between two waves is the horizontal distance a similar part of one wave leads or lags the other wave
Phase difference is measured in fractions of a wavelength, degrees or radians
How to find phase difference?
This can be found from the relative position of the crests or troughs of two different waves of the same frequency
What is in phase?
When the crests of each wave or the troughs of each wave are aligned, the waves are in phase
In phase is 0 degrees, a phase difference of 360 degrees is a time delay of one cycle which amounts to no phase shift at all
What is anti-phase?
When the crest of one wave aligns with the trough of another, they are in antiphase
In anti-phase is 180 degrees or π radians
What is the total energy of an object oscillating with SHM? Mention equation
The total energy of an object oscillating with SHM is the sum of its potential energy (gravitational or elastic) and kinetic energy
E = EP + EK
Where:
E = total energy in joules (J)
EP = potential energy in joules (J)
EK = kinetic energy in joules (J)
Which forms of energy are at maximum or minimum at the point of maximum displacement from the equilibrium position?
The potential energy store of the object is at a maximum at the point of maximum displacement from the equilibrium position
The point of maximum displacement is amplitude x0
Kinetic energy is zero at amplitude
Potential energy is equal to the total energy of the system at this point
What happens to energy as the oscillating system returns to equilibrium position from maximum displacement?
Energy is transferred from the object’s potential energy store to its kinetic energy store as the object moves from amplitude to the equilibrium position
The object has both potential and kinetic energy
The sum of the potential and kinetic energy is equal to the total energy of the system
The total energy of the system is conserved
Which forms of energy are at maximum or minimum at the equilibrium position and why?
The kinetic energy store of the object is at a maximum at the equilibrium position
This is because velocity is at a maximum as the object passes through the equilibrium position
Kinetic energy is equal to the total energy of the system at this point
What happens to energy as the oscillating system travels to the maximum displacement from equilibrium?
Energy is transferred from the object’s kinetic energy store to its potential energy store as the object moves from the equilibrium position to amplitude
The object has both potential and kinetic energy
The sum of the potential and kinetic energy is equal to the total energy of the system
The total energy of the system is conserved
The defining conditions of simple harmonic oscillations are that the restoring force and the acceleration must always be:
Directed towards the equilibrium position, and hence, is always in the opposite direction to the displacement
Directly proportional to the displacement
a ∝ −x
Relationship between force and displacement in SHM and graph
Force and displacement in SHM have a linear relationship where the gradient of the graph represents the constant
In this case, the spring constant k. Negative slope line passing through origin
Define displacement
Displacement (x) of a wave is the distance of a point on the wave from its equilibrium position
It is a vector quantity; it can be positive or negative and it is measured in metres (m)
One complete oscillation is:
1 wavelength
360°
2π radians
The displacement-time graph for an object moving with SHM is a sinusoidal curve if
The object starts to oscillate from the equilibrium position.
The equilibrium position is x = 0 at t = 0
The displacement-time graph is a cosine curve if
he object starts to oscillate from the position of maximum displacement.
Maximum displacement is x = x0 at t = 0
What do the maxima and minima indicate in displacement time graphs?
The maxima and minima on the graph are the values of maximum displacement (x0) of the oscillating object on either side of the equilibrium position
What does the gradient give in displacement time graphs of SHM
It gives the velocity by drawing a tangent to a point on the graph
The velocity-time graph is a cosine curve if
The object starts to oscillate from the equilibrium position when x = 0 at t = 0
The displacement-time graph is a sine curve
The velocity-time graph is a sine curve if:
The object starts to oscillate from the position of maximum displacement when x = x0 at t = 0
The displacement-time graph is a cosine curve
What is the phase difference between displacement-time graph and velocity-time graph?
90 degrees or π/2 rad. (velocity time graphs have a contrasting trigonometric function graph to the displacement time graph)
What do the maxima and minima indicate in velocity time graphs?
The maxima and minima on the graph are the values of maximum velocity (v0) of the oscillating object as it passes the equilibrium position
How is the acceleration time graph obtained?
The acceleration-time graph is obtained by taking the gradients of tangents to all points on the velocity-time graph. Therefore acceleration is the gradient of a velocity-time graph for SHM
The acceleration-time graph is a negative sine curve if:
The object starts to oscillate from the equilibrium position when x = 0 at t = 0 (when displacement-time graph is sine curve)
The acceleration-time graph is a negative cosine curve if:
The object starts to oscillate from the position of maximum displacement when x = x0 at t = 0 (when displacement-time graph is cosine curve)
What do the maxima and minima indicate in acceleration time graphs?
The maxima and minima on the graph are the values of maximum acceleration (a0) of the oscillating object at the positions of maximum displacement (x = x0)
Phase difference between displacement-time and acceleration-time graphs of SHM
180 degrees or π
State one similarity and two differences between the graphs
Note that all graphs must have the same period
The only two differences between the graphs are:
The shift in time - i.e. there is a phase difference of 90° between successive graphs
The amplitude of the wave form - i.e. the different amplitudes of the three graphs are the values of maximum displacement x0, maximum velocity v0 and maximum acceleration a0 of the oscillating object
