Oscillation
Continuously repeated movements
Period (T)
The time taken for an object to complete one full oscillation
Simple harmonic motion
The motion of an oscillating system.
There’s usually restoring force during the SHM, which tries to return the object to its Centre position
Restoring force
F = -kx
Where the force is proportional to the distance from the center position and k is a constant that depends on the particular oscillating system
Amplitude
The maximum displacement from the equilibrium position
Period of a pendulum
T = 2π√l/g
Where L is the length of the pendulum string
Angular velocity
• ω = θ/t
Where t is the time in seconds
• ω = 2πf
• ω = 2π/T
Where T is the period
Horizontal distance
x = r cosθ
Moving in a circle
x = r cos(ωt)
R can also be amplitude
ω of a pendulum is √g/L
L is the length of the string of the pendulum
ω of a string is √k/m
K is the restoring force constant
Acceleration acts in the opposite direction to the displacement
When displacement is zero so is the acceleration
And when X is max so is acc
The displacement graph is a cosine graph
The acceleration graph is a negative cosine graph
The velocity is a negative sine graph
During a swinging motion of a pendulum, at each end of the swing, it’s velocity is zero
So it has zero kinetic energy and a maximum potential energy at this point
When the bob passes through the central position, it’s velocity is at a maximum
And the kinetic energy is at a maximum while the potential energy is at a minimum
Free oscillation
A continuous exchange of PE and KE, caused by a restoring force which is proportional to the displacement.
Natural frequency
The frequency at which the oscillating system naturally oscillates without external forces
Forced oscillation
Forcing the the oscillating system to oscillate at another frequency than its natural one.
The frequency is called driving frequency
Damped oscillations
These suffer a loss of energy in each oscillation reducing the amplitude over time
Types of damping:
Under damping
Over damping
Critically damped (overshooting)
Under damping
It’s when the oscillator completed several oscillations and the amplitude decreases exponentially
E.G. A normal pendulum
Overdamping
The amplitude of the oscillation may drop so rapidly that the oscillator does not even complete one cycle
E.g. under water
Critical damping or overshooting
When the oscillator returns to its equilibrium position in the quickest possible time without going past that position
Undamped oscillation
Is when no energy is lost during oscillations
Resonance
Is when a system is forced to vibrate at its natural frequency, absorbing more and more energy and thus increasing the amplitude.
A simple setup of several pendulums can demonstrate resonance. They heavy swinging ball acts through the suspension wire to drive all the other pendulums at its natural frequency.
Only the pendulum with the same natural frequency will vibrate with a large amplitude. The pendulum has the same length of wire as the driving pendulum. The other pendulums show little movement because the driving frequency doesn’t match their natural frequency
As the driving frequency applied to an oscillating system changes, it will pass through Natural frequencies of the system which causes large amplitude vibrations
The size of the vibrations at resonant frequencies can be so great that they damage the system
