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Harmonic Oscillators in Context Any oscillations about an equilibrium where its restoring force is proportional to its displacement will be simple harmonic This doesn’t apply just to pendulu...
What is an imaginary number? What is a complex number? What is Cartesian Form? There are a number of different forms that complex numbers can be written in The form?z?=?a?+?bi is known as?Cartesian...
Period of Simple Pendulum A simple pendulum is another type of simple harmonic oscillator The pendulum consists of a string and a bob (a weight, generally spherical) at the end The?ti...
Period of Mass-Spring System A mass and spring system is a type of simple harmonic oscillator The?time period?of a mass-spring system is given by: Where: T?= time period (s) m?= mass (kg) k?...
Maximum Speed The speed?v?of an oscillator will vary in SHM. It is: Maximum?at the?equilibrium?position (x?= 0) Zero?at the?amplitude?(x = A) The maximum speed,?vmax, is given by the equatio...
SHM Graphs The displacement, velocity and acceleration of an object in?simple harmonic motion?can be represented by graphs against time All undamped SHM graphs are represented by?periodic fu...
Conditions for Simple Harmonic Motion Simple harmonic motion (SHM)?is a specific type of oscillation An oscillation is said to be SHM when: The acceleration is proportional to the displaceme...
?What are Permutations? A?permutation?is the number of possible arrangements of a set of objects when the?order?of the arrangements matters A permutation can either be finding the number of ways to...
Calculating Centripetal Force An object moving in a circle is not in equilibrium, it has a resultant force acting upon it This is known as the?centripetal force?and is what keeps the object ...
Calculating Centripetal Acceleration Centripetal acceleration is defined as: The acceleration of an object towards the centre of a circle when an object is in motion (rotating) around a circ...
Angular Speed Any object travelling in a uniform circular motion at the same speed travels with a?constantly changing velocity This is because it is?constantly changing direction, and is the...
