Simple Harmonic Motion and Gravitation

Simple Harmonic Motion

Description of a bob - Starting from the equilibrium position, it moves in one direction, back to equilibrium and moves in the other direction, and back to equilibrium again.

At centre - displacement = 0 , velocity = max , acceleration = 0

At the maximum displacement - displacement = amplitude , velocity = 0 , acceleration = max

SHM - the acceleration is proportional to the displacement from a fixed point and is directed towards that fixed point.

ω is the constant of proportionality.

The negative sign is directed towards the fixed point.

Damping is the process whereby energy is taken from the vibrating system to minimise the effect of resonance.

Under and heavy damping quickly reduces the amplitude to zero.

Critical damping reduces the amplitude in the shortest possible time.

Over damping takes longer for the amplitude to reach zero than critical damping.

Displacement is the distance in a given direction.

Amplitude is the maximum displacement from equilibrium of an oscillating object.

Period is the time for 1 oscillation.

Frequency of an oscillating object is the number of cycles of oscillations per second.

Phase difference is measured in radians, for 2 objects oscillating with the same time period (T), where phase 

difference is 2 π t / T

Resonance is the amplitude of vibration of an oscillating system which is subjected to a periodic force which is 

largest when the periodic force has the same frequency as the resonant frequency of the system.

Periodic force is a force that varies regularly in magnitude with a definite time period.

Resonant frequency is the frequency of an oscillating system in resonance.

Gravitation

Gravitational fields are only attractive.

Gravitational field strength is the point in a body’s field as the force is exerted on an object placed at that point 

per kilogram of the objects mass.

GPE is the energy of an object due to its position in the gravitational field.

GPE is zero at infinity as the object is so far away that the effect of gravity is negligible.

GPE is negative on the surface of the Earth as an object needs energy to overcome the gravitational field.

GPE is the work done to move a small object from infinity to that point.

Gravitational potential at a point in a gravitational field is the work done per unit mass to move a small object 

from infinity to that point.

Radial Field is where field lines are straight and converge as if from a single point over a large distance.

Uniform field is a region where the field strength is the same in magnitude and direction at every point in the field over a small distance.

The potential gradient at a point in a gravitational field is the change in potential per metre at that point.

Equipotentials are lines of equal potential.

Equipotential surfaces are perpendicular to field lines.

Kepler’s law states that T² is proportional to r³.

Geostationary satellites stay over the equator with a circular orbit which takes 24 hours to fully orbit the Earth in the same direction.

Geosynchronous satellites repeatedly orbit regular points over the Earth over time.

Newton’s law of gravitation states the gravitational force between two point masses at distance apart is given by F = G m M / r².

©2011 Grant Dwyer