18 Simple Harmonic Motion Flashcards
Time period
Oscillating motion is the time for one complete cycle of oscillation
Frequency
Oscillations in the number of cycles per seconds made by oscillating object
Ψ
Angular frequency
2π / t
Displacement
Of an object from equilibrium continually changes during the motion
Phase difference
2πΔt / T
( in radians)
The time between successive instants when the two objects are at maximum displacement in the same direction
Variation of velocity with time
Magnitude of the velocity is greatest when the gradient of the displacement-time graph is greatest
Velocity is zero when the displacement-time graph is zero
Variation of acceleration with time
(Given by the gradient of the velocity-time graph)
Acceleration is greatest when the gradient of velocity-time graph is greatest, this is when the velocity is zero and maximum displacement
Acceleration is zero when the gradient of the velocity-time graph is zero. ( displacement is zero and velocity at maximum)
Acceleration is always in the opposite direction to the displacement
True or false?
True
Simple harmonic motion (conditions)
Proportional to displacement
Opposite direction to the displacement
a = -x
Acceleration
a = -ω^2 x
State two quantities that increase when the temperature of a given mass of gas is increased at a constant volume
Pressure and kinetic energy
What assumptions are made when using the equation Q=ml
No heat is loss to the surrounding
100% efficient
Simple harmonic motion
Acceleration is proportional to displacement
Direction is opposite to displacement
Why is the motion is no longer simple harmonic motion
Bungee cord becomes slack
Motion under gravity
Constant acceleration
Where on the bungee cord is the stress at a maximum
Stress = F/A
Force at this point includes the whole cord
Larger amplitude ( pendulum)
Reduces air resistance
Longer time period ( pendulum)
Reduces uncertainty in reaction time
Uniform circular motion
When an object rotates at a steady rate / speed
Angular speed
Angle displacement per second
Angular displacement
Angle turned through in a time
Centripetal acceleration
Acceleration of an object in uniform circular motion
Free oscillation
A freely oscillating object oscillates with a constant amplitude
No frictional forces
Damping
Damping occurs when frictional forces cause the amplitude of an oscillation to decrease
Light damping
In this case the amplitude gradually decreases with time
Critical damping
In this case the system returns to equilibrium without overshooting, in the shortest possible time after it has been displaced from equilibrium
Heavy damping
Returns to equilibrium more slowly than the critical damping case
Forced vibration
Vibrations of the system subjected to an external force
Resonance
The amplitude of vibration of an oscillating system subjected to a periodic force is largest when the periodic force has the same frequency as the resonant frequency of the system
Resonant frequency
The frequency of an oscillating system in resonance
Applied frequency of the periodic force
Is equal to …
The natural frequency of the system
Phase difference between displacement and the periodic force is …
1/2π
Resonance ( lighter the damping)
Larger the maximum amplitude becomes at resonance
Closer the resonant frequency is to the natural frequency of the system
Amplitude
Oscillations is the maximum displacement of the oscillating object. Form equlibrium
free vibration
vibrations where the is no damping and no periodic force acting on the system, so the amplitude of the oscillations is constant
sinusoidal curves
any curve with the same shape as a sine wave
periodic force
a force that varies regularly in magnitude with a define time period
applications of simple harmonic motion
T = KΔL
a = -kx / m
a = -Ψ^2x
(object would oscillate in a simple harmonic motion )
T=2π √ m/k
what determines the frequency of oscillation of a loaded spring?
adding extra mass
using a weaker spring
simple harmonic motion speed equation
(Ek=1/2mv^2)
v= ±√ (A^2 -x^2)
(x=0 would give the maximum speed)
energy displacement graph
Ep = 1/2 kx^2
kinetic energy of inverted parabola
Ek = Et -Ep
= 1/2 k(A^2 -x^2)
for a oscillating frequency system with little or no damping at resonance
the applied frequency of the periodic force = the natural frequency of the system
bridge oscillations
bridges can oscillate because of the springs and it mass
a cross wind can form a force on a bridge, if the wind speed is such that the periodic force is equal to the natural frequency, resonate can occur
a steady trail of people in step with each other walking across a footbridge can cause resonant oscillations of the bridge span if there is not enough damping
max speed
ωA
max acceleration
ω^2 A
