Chapter 14 - Periodic Motion Flashcards
What is periodic motion?
Motion that repeats itself in an indefinite cycle.
When does periodic motion occur?
Whenever a body has a stable equilibrium position and restoring force that acts when the body is displace from equilibrium.
What is the period?
T
Time for one cycle.
What is frequency?
f
Number of cycles per unit time.
What is angular frequency?
Omega
2pi*f
Formula for angular frequency:
Omega = 2pi*f = 2pi/T
What is Simple Harmonic Motion? SHM
When the restoring force F_x in periodic motion is directly proportional to the displacement x, the motion is called SHM.
In SHM, what depends on mass m and force constant k?
Nothing depends on amplitude.
Angular frequency
Frequency
Period in SHM
Which features of SHM are sinusoidal functions of time?
Displacement
Velocity
Acceleration in SHM
What are the Amplitude A and phase angle of the oscillation determined by?
Initial displacement
Velocity of the body
Formula for displacement?
x= Acos(omega*t + phase angle)
Energy is conserved in SHM, the total energy can be expressed in terms of?
Force constant k and amplitude A
E=0.5mv^2 + 0.5kx^2 = 0.5kA^2 = constant
In angular SHM the frequency and angular frequency are related to:
The moment of inertia
Torsion constant k
Formulas for angular SHM:
Omega = Sqrt(torsion constant/inertia) Frequency = 1/2pi Sqrt(torsion/inertia)
A simple pendulum consists of:
Point mass m at the end of a massless string of length L.
In a simple pendulum, what does the angular frequency, frequency and period depend on?
g and L
What is a physical pendulum?
Any body suspended from an axis of rotation.
In a physical pendulum what is the angular frequency and period for small amplitude oscillations dependant on?
Mass
Distance from the axis of rotation to the centre of gravity
Moment of inertia
Formulas for a physical pendulum:
Angular frequency = Sqrt (mgd/I)
Period = 2pi*above
What causes a damped oscillation?
When a force F =-bv is added to a simple harmonic oscillator.
If b < 2SQRT(km)
Underdamping
The system oscillated with a decaying amplitude and an angular frequency (omega dashed) that it lower than it would be without damping.
If b= 2SQRT(km)
Or b>2SQRT(km)
Critical damping
Or Over damping
When the system is displaced it returns to equilibrium without oscillating.
What is forced/driven oscillation?
When a sinusoidally varying driving force is added to a damped harmonic oscillator.
What is resonance in driven oscillations?
The amplitude is a function of the driving frequency and reaches a peak at the driving frequency close to the natural frequency of the system. This behaviour is resonance.
