Harmonic Motion Flashcards
What is simple harmonic motion?
When an object oscillates on either side of a midpoint
What is the condition of simple harmonic motion?
The restoring force ( force bringing the object back to midpoint) is directly proportional to its displacement from the midpoint but in the opposite direction
F = -kx
Graphs representing x ,v and a
x = Aωcos(ωt ) or a cos graph
v = -Aωsin(ωt) or it’s respective sin graph
a= -Aωcost(ωt)
MATHS:
ds/dt = v
d2s/dt2 = a so differentiation stuff :)
What is the formula for angular frequency?
ω = 2πf or 2π/T
How to find the Amplitude?
It’s the maximum displacement of the graph
How to find the velocity?
v= Aω
other equation for acceleration?
a = -xω^2
Relationship between the frequency and the amplitude in SHM?
there isn’t any relationship (single :(( )
How to find the period of a mass-spring system in simple harmonic motion?
T = 2π *sqrt(m/k)
k is spring constant
How to find the period of a pendulum in simple harmonic motion?
T =2π *sqrt(l/g)
l is length of string
What are free oscillations?
When SHM occurs at its natural frequency
No energy is transferred to the surroundings
Same amplitude forever
Forced oscillations?
When there needs to be a driving force to maintain SHM
What is resonance?
When the driving frequency is the same as the natural frequency
This causes a maximum amplitude where they are resonating
Maximum energy transfer
What is damping?
When energy is lost to the surroundings in SHM
Reducing the amplitude
What does damping do?
It reduced the amplitude of the oscillations (no effect on frequency)
