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

How is potential energy affected during SHM

Minimum at equilibrium, maximum at highest displacement

Draw the graph of displacement against kinetic and potential energies

good

Free Oscillation

There is no external, periodic force being applied to the object. The system oscillates at its natural frequency

Natural frequency

The frequency a system will oscillate at when undergoing free oscillation

Forced Oscillation

A periodic driving force is applied to the system causing it to oscillate at the same frequency as the driving force

Driving frequency

The frequency with which the driving force is applied to the oscillating object