17.1 - 17.5 Flashcards
what is simple harmonic motion
oscillating motion in which the acceleration is directly proportional to the displacement and is directed towards a fixed point.
key features of simple harmonic motion
acceleration is directly proportional to the displacement
the acceleration is in the opposite direction to the displacement
define isochronous oscillator
oscillator with the same period regardless of the amplitude
what are the equations that are solutions to the simple harmonic motion equation? when is each used?
x = Acos(ωt) or x=Asin(ωt)
x: displacement, ω: angular frequency, t: time, A: amplitude
the cos version is used if at t=0 the object is at its amplitude
the sin version is used if at t=0 the object is its equilibrium position
how does the velocity of SHM change with angular frequency if the amplitude is kept constant
increasing angular frequency(ω) decreases the time for the object to oscillate with the same amplitude. so velocity increases
how does the velocity of SHM change with amplitude if the angular frequency is constant
if the frequency is the same but amplitude increases, a greater distance is travelled in the same amount of time. so velocity increases
how does energy change in SHM
at the amplitude, it has zero kinetic energy. it’s all GPE. as it moves towards the equilibrium position it gains KE. at the equilibrium position it has max KE and zero GPE
define ‘damping’
when an external force acts on an oscillating object, reducing the amplitude
what’s the difference between light/heavy/very heavy damping
light: small external force. a gradual reduction in amplitude
heavy: larger external force. fast reduction in amplitude
very heavy: causes no oscillatory motion. the object moves from its amplitude to the equilibrium position
define ‘free oscillation’
when a mechanical system is displaced from its equilibrium position and allowed to oscillate without any external forces
define ‘forced oscillation’
an oscillation in which a periodic driver force is applied to the oscillator
define ‘resonance’
an increase in the amplitude of a forced oscillation when the driving frequency matches the natural frequency of the system. often causes it to break
whats the natural frequency of a forced oscillator
the natural frequency equals the driving frequency (frequency of the driving force)
uses of resonance
clocks use the resonance of a pendulum
instruments bodies resonant to make louder sounds
some radios use it to find the correct frequency signal
Magnetic resonance imaging (MRI) harmlessly scan us
