oscillations Flashcards
describe simple harmonic motion (SHM)
-object oscillates either side of an equilibrium point
-a restoring force is always acting on the object in the direction of the equilibrium point
-the force is proportional to the displacement, which also means the object has an acceleration proportional to the displacement
SHM equations
F=-kx
a=-xw^2
angular velocity equations
spring oscillators
a mass on a string oscillating by SHM
spring oscillator time period equation
T=2πroot m/k
what are spring oscillator’s time periods unaffected by
gravity and displacement
pendulum oscillators
a mass on a string oscillating with simple harmonic motion
pendulum oscillator time period
T=2πroot l/g
what is a pendulums time period unaffected by
mass and displacement
what is the gradient of a displacement time graph
velocity
what is the gradient of a velocity time graph
acceleration
what is energy transferred between during SHM
kinetic energy and potential energy
potential energy max during SHM
during the maximum displacement and negative displacement
where is kinetic energy max in SHM
at the point of equilibrium, where the displacement is 0
what is the sum of the kinetic and potential energy in SHM equal to
the total energy in the system
what is damping
where energy is transferred out of a system
what are natural causes of damping
friction and air resistance
where might damping be wanted
spring doors, speedometers, car suspensions, swings
types of damping
light damping, critical damping and over damping
what is light damping
the oscillations are reduced slowly (air resistance and friction are an example)
what is critical damping
stopping oscillating and returning to oscillations as soon as possible
what is over damping
damping force greater than critical damping, but takes longer to return to the equilibrium position
Types of vibrations
free vibrations and forced vibrations
what are free vibrations
the frequency the system tends to vibrate at in a free vibration is called the natural frequency
what is resonance
when the frequency of the driving force is equal to the natural frequency
what are forced vibrations
a driving force causes the system to vibrate at a different frequency
what does resonance do to the amplitude
the amplitude of oscillations is at a max
what does resonance do to energy
the rate of energy transfer is at a max
is the driving force out of phase during resonance
yes, by π/2 and ahead of oscillations
