What factors affect the rate at which my spring Oscillates - page 1
Keywords: What factors affect the rate at which my spring Oscillates
By Carlitob10 on 04/11/2006 12:04:33
Level: A Level (Year 13)
Page Number: 1 of 9 pages: 1 2 3 4 5 6 7 8 9
Investigation of a loaded spring Oscillator
Aim: To investigate what factors affect the period oscillations of a mass-spring system when it is in simple harmonic motion.
Backgrounds knowledge
Simple Harmonic Motion
Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. The motion is periodic as it repeats itself at standard intervals in a specific manner described being sinusoidal, with constant amplitude. It is characterised by its amplitude which is always positive and depends on how motion starts initially, its period which is the time for a single oscillation and its phase which depends on displacement as well as velocity of the moving object.
The requirements for s.h.m of a mechanical system are:
1. a mass that oscillates;
2. a central position where the mass is in equilibrium;
3. a restoring force that acts to return the mass to the central position (the restoring force is proportional to the distance of the mass from the equilibrium position).
Formulae in Simple Harmonic Motion
Consider an object round a circle of radius and centre Z with a uniform angular velocity ω, Diagram 1.
Diagram 1
If CZF is a fixed diameter, the foot of the perpendicular from the moving object to this diameter moves from Z to C, back to Z and across to F, and then returns to Z, while the object moves once round the circle from O in an anti-clockwise direction. The to and fro motion along CZF of the foot of the perpendicular is defined as simple harmonic motion.
Suppose the object moving round the circle is at A at some instant, where angle OZA = , and suppose the foot of the perpendicular from A to CZ is M. The acceleration of the object at A is ω2r, and this acceleration is directed along the radius AZ. Hence the acceleration of M towards Z
= ω2r cos AZC = ω2r
But r sin = MZ = y say.
acceleration of M towards Z = ω2r.
Now ω2 is a constant.
acceleration of M towards Z distance of M from Z.
If mathematically, we express that the acceleration is always directed towards Z, we must say
acceleration towards Z = – ω2y (1)
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