Chapter 5.3 - Oscillations Flashcards
Displacement
The distance an object is from it’s rest position
Amplitude
Maximum displacement
Frequency
The number of oscillations per unit time at any point
Angular Frequency and its symbol
(ω) The product 2pi*f
Phase Difference and its symbol
(Φ) The fraction of a complete cycle between two points, expressed in radians
Simple Harmonic Motion
An oscillating body where the acceleration of the body is directly proportional to its distance from a fixed point (its equilibrium position) and this acceleration is always directed to the fixed point
SHM defining equation
a=-(ω^2)x
Solutions to the equation a=-ω^2x
x = Acosωt, x = Asinωt
Equation for velocity
v = +-ω*root(A^2-x^2)
Maximum acceleration
(Sub in A for x) max a = Aω^2
Maximum velocity
(Sub in A for x) max v = Aω
Maximum displacement
A
Investigation for SMH
Set up a mass on a spring hanging from a clamp stand. Place a position sensor beneath it. Pull down the spring and let it oscillate with its displacement being recorded. When plotted against time it should resemble a sine wave with decreasing amplitude.
What effect does increasing the mass on a spring have on SHM time period
Longer time period
What effect does the stiffness of the spring have on SHM time period
High stiffness = short time period
What effect does increasing the initial displacement have on SHM time period(with a spring)
No effect on time period
What effect does increasing the initial angle of a pendulum have on SHM time period
No effect on time period
What effect does increasing the mass of a pendulum have on SHM time period
No effect on time period
What effect does increasing the length of the string of a pendulum have on SHM time period
Increases time period
Relationship between period and amplitude of SHM
They are independent
How is angular frequency related to angular velocity
Angular frequency is the magnitude of the angular velocity
If x = Asinωt what is velocity and acceleration
v = ωAcosωt a =-ω^2Asinωt (just differentiate)
How is mechanical energy affected during SHM
Not affected
How is kinetic energy affected during SHM
Maximum at equilibrium, minimum at highest displacement
