What is simple harmonic motion?
An oscillation in which the acceleration of an object is directly proportional to its displacement from the midpoint, and is directed towards the midpoint.
What does the size of the restoring force depend on?
The size of the restoring force depends on the displacement, and the force makes the object accelerae towards the mid point.
Explain the transfer of energy in oscillating pendulum.
As the object moves towards the midpoint, the restoring force does work on the object and so transfers some PE to KE. When the object is moving away from the midpoint, all that KE is transferred back again to PE again.
At what points in an oscillating pendulum is the KE and PE maximum?
At midpoint, the object's PE is zero and its KE is maximum.
At maximum displacement (the amplitude) on both sides of the midpoint, the object's KE is zero and its PE is maximum.
The sum of the potential and kinetic energy in an oscillating system is always what?
The sum of the PE and KE is always constant and is known as the mechanical energy.
As long as motion is not damped.
Draw an energy-time graph for an oscillating pendulum for both its PE, KE and total energy.
Draw the displacement,velocity and accelarations graphs against time. Explain what the maximum value of each graph is.
Velocity,v, is the gradient of the displacement-time graph (dx/dt). It has a maximum value of (2πf)A. It is a quarter of a cycle in front of the displacement.
Acceleration,a, is the gradient of the velocity-time graph (d2x/dt2). It has a maximum value of (2πf)2A, and is in antiphase with the displacement.
What is the frequency of SHM?
It is the number of oscillations per second.(Measured in Hz).
What is the period?
The period, T, is the time taken for a complete cycle in seconds.
What are frequecy/period independant of?
The are independant of the amplitude. So a pendulum clock will keep ticking in regular time intervals even if its swing becomes very small.
What is the equation that gives the acceleration of SHM?
d2x/d2t = -(2πf)2x
What is the equation that gives the value of the displacement when someone starting the stopwatch with a pendulum at maximum displacement.
x = Acos(2πft)
What is the equation that gives the displacement for someone releasing a pendulum but starting the stopwatch as the pendulum swings through the midpoint?
x = Asin(2πft)