 # Section 3.6.1 Further mechanics: Periodic motion Syllabus Extract You should be able to:
3.6.1.1 Circular motion

Motion in a circular path at constant speed implies there is an acceleration and requires a centripetal force.

Direction of angular velocity will not be considered.

Angular speed - ω

#### ω =v/r= 2πf

Centripetal acceleration - a

#### a = v2/r = ω2r

Centripetal force

#### F = mv2/r = mω2r

The derivation of a = v 2/r will not be examined.

Remember that acceleration is rate of change of velocity - and velocity is a vector - it has direction as well as magnitude of speed associated with it.

With circular motion the object is being constantly pushed towards the circular path's centre - that is the direction of the acceleration. Circular Motion Multiple Choice

Questions on circular motion link to gravitational fields - motion of planets and satellites.

MS 0.4 Estimate the acceleration and centripetal force in situations that involve rotation.

3.6.1.2 Simple harmonic motion (SHM)

Analysis of the characteristic features of simple harmonic motion. Graphical representations linking x,v,a and t

Velocity as gradient of displacement-time graph and acceleration as the gradient of the velocity-time graph..

Maximum speed = ωA

Maximum acceleration = ω2A

Ensure you can define SHM - they always ask for that - 2 marks!

Get an overall appreciation of displacement from mean position, velocity and acceleration changes.

Remember that ω = 2πf   AT i, k Data loggers can be used to produce s − t, v − t and a − t graphs for SHM.

MS 3.6, 3.8, 3.9, 3.12 Sketch relationships between x, v, a and a − t for simple harmonic oscillators.

3.6.1.3 Simple harmonic systems

Study of mass-spring system: Study of simple pendulum: Questions may involve other harmonic oscillators (eg liquid in U-tube) but full information will be provided in questions where necessary.

Effects of damping on oscillations.

Practical techniques must be appreciated - this is an opportunity for the examiner to check your experimental techniques. SHM Multiple choice

Required practical 7: Investigation into simple harmonic motion using a mass–spring system and a simple pendulum.

MS 4.6 / AT b, c Students should recognise the use of the small-angle approximation in the derivation of the time period for examples of approximate SHM.

3.6.1.4 Forced vibrations and resonance

Qualitative treatment of free and forced vibrations.

Resonance and the effects of damping on the sharpness of resonance.

Examples of these effects in mechanical systems and stationary wave situations.

This leads to 'wordy' answers, ensure you understand all of the terms and can define them with precision.

AT g, i, k AT g, i, k Investigation of the factors that determine the resonant frequency of a driven system.

Phase difference between driver and driven displacements has been removed from the syllabus but is interesting to look at!