Simple Harmonic Motion Flashcards
What is simple harmonic motion?
a common type of oscillation where an object vibrates about an equilibrium position under the influence of an unbalanced force
What must be true about the unbalanced force in simple harmonic motion?
- always directed towards the equilibrium position
* proportional to the displacement of the object from the equilibrium position
What are the equations for simple harmonic motion?
- y=Awsinwt
- y=Awcoswt
- a=-w²y
- F=-kx
What is the relationship between the spring extension and tension?
the spring extension is directly proportional to the tension in the spring
How is the constant of proportionality represented?
k
What is the opposing equal force to the stationary mass in equilibrium?
the resting force
What can be said about spring constant and resting force?
they are equal
What is the symbol for the spring constant?
k, it has the units Nm⁻¹
What is the equation for Hooke’s law?
F=ky
What is the amplitude?
the maximum displacement of an oscillating object from the zero displacement (equilibrium) position
What is the frequency of the SHM?
the number of complete oscillations performed
For an object to be performing simple harmonic motion what must the net force acting on it be proportional to?
displacement
What quantity is continuously changing as an object oscillates?
acceleration
What happens as the displacement of the mass increases?
the velocity decreases therefore the kinetic energy of the mass decreases
What happens to the lost energy in SHM?
it is stored as potential energy in the spring
What is the relationship between elongation and potential energy?
The more the spring is stretched or compressed the greater the potential energy stored in it
What is the case when the kinetic energy is at a maximum?
when the speed of an oscillating object is at a maximum, this is when the displacement (y) =0
What happens when y=a?
- the velocity is momentarily zero and so the kinetic energy is zero
- the restoring force acting on the object is at a maximum at this point and so the potential energy is at a maximum
A mass attached to a spring is oscillating horizontally on a smooth surface. At what point in its motion does kinetic energy have a maximum value?
when the displacement from the rest position is zero
What does A equal?
amplitude
What is the equation for kinetic energy?
Ek=1/2mw^2(A^2-y^2)
What is the equation for potential energy?
Ep=1/2mw^2y^2
What happens as a SHM system vibrates?
energy is converted between potential (Ep) and kinetic (Ek)
What can be said about the energy of waves?
The energy of the waves is directly proportional to the square of the amplitude
What is the intensity/irradiance?
The amount of energy per second per unit area
What is power?
The amount of energy per second
What is the equation for intensity?
I=P/A
What is intensity directly proportional to?
The square of the waves amplitude
What does a phase difference of a whole number result in?
Perfectly constructive interference
What is perfectly constructive interference?
Peak meets peak and trough meets trough
What does a phase difference of n+1/2 result in?
Perfectly destructive interference
What is perfectly destructive interference?
Peak meets trough and trough meets peak
In perfectly destructive interference what is the amplitude?
The amplitude of the combined wave is 0m
What is the amplitude of a perfectly constructive interference?
The amplitude of the combined wave is 2A
What is damping?
When the amplitude of oscillation of a pendulum gradually decreases to zero due to air resistance
What happens to the total energy of a system during damping?
The total energy of the pendulum will decrease to zero
What happens to the amplitude during damping?
The amplitude decreases with each half-damped oscillation
What is the phase difference?
A measure of the separation of these two points as a fraction of the wavelength and expressed as an angle in radians
What happens if the amplitude of a wave doubles?
The intensity of the wave increases four times
What are nodes?
Positions of zero disturbance in a stationary wave
What does the distance between nodes equal?
Half a wavelength
What are points of maximum disturbance called?
Antinodes
What causes a stationary wave to form?
By the superposition (or overlapping) of the incident wave and the reflected wave
When does an object not have a simple harmonic motion?
When the acceleration(a) or force(F) is directly proportional to the negative displacement from the equilibrium position. This can’t be described as SHM as the object has a constant speed.
When does the maximum potential energy in SHM occur?
When y has a maximum value i.e y=A
What can be said about Ek when Ep is at a maximum?
Ek is at a minimum
What can be said about the energy of travelling waves?
It is directly proportional to the square of the amplitude
Do you know the equation to calculate the phase difference?
2pix/wavelength
What is the disturbance?
The height of the combined wave
What are coherent waves?
Waves with the same path difference
What does a phase difference of a whole number multiple of 2 π result in?
Perfectly constructive interference
What does a phase difference of (n+1/2)x2 π result in?
Perfectly destructive interference
What do we associate standing waves with?
Musical instruments
What is the first harmonic often referred to?
The fundamental
What does the wavelength of any node equal?
The distance between adjacent nodes x2
What does the amplitude of oscillation depend on?
Particle position
