2. Simple harmonic motion Flashcards
Define oscillation:
The repetitive variation with time t of the displacement x of an object about the equilibrium position
What is the equilibrium position?
The position where there is no resultant force acting on an object
What is meant by the displacement of a wave?
It is the distance of a point on the wave from its equilibrium position
What is meant by the amplitude of a wave?
It is the maximum value of the displacement on either side of the equilibrium position
Define wavelength:
The length of one complete oscillation measured from the same point on two consecutive waves
How can you calculate the time period for SHM?
- T = 1 / f
- T = 2π / ω
Define frequency:
The number of oscillations per second
Define angular frequency:
The rate of change of angular displacement with respect to time
What is meant by the phase difference?
It is a measure of how much a point or a wave is in front or behind another
How can you calculate the phase difference?
Define simple harmonic motion:
SHM is a specific type of oscillation that occurs when acceleration is proportional to displacement from a fixed point and in the opposite position
What is meant by the restoring force in SHM?
The restoring force produces the acceleration, is always acts towards the equilibrium position and is proportional to the displacement of the object in SHM
How do you calculate the acceleration of an object in SHM?
a = -ω^2 * x
When is the acceleration its maximum in SHM?
When the displacement is at a maximum or at its amplitude
What is the displacement equation for an object in SHM?
x = x0 * sin(ωt)
x0 = amplitude
t = time
When is the displacement of an object in SHM at its maximum?
When sin(ωt) equals 1 or -1, when x = x0
What is the speed equation for an object in SHM?
v = v0 * cos(ωt)
v0 = maximum speed
ω = angular frequency
t = time
What is the equation for an object in SHM relating the speed and amplitude?
v = +/- ω * √(x0^2 - x^2)
How do you calculate the maximum speed of an object in SHM?
v0 = ωx0
When does an object in SHM reach its greatest speed?
When the object reaches the equilibrium position or when its displacement is 0
How are the graphs of the velocity-time, displacement-time, acceleration-time graphs related?
- Velocity-time graph = gradient of displacement-time graph
- Acceleration-time graph = gradient of velocity-time graph
What is the shape of an SHM displacement-time graph?
A sine curve
What is the shape of an SHM velocity-time graph?
A cosine graph that is 90° out of phase with the displacement-time graph
What is the shape of an SHM acceleration-time graph?
A negative sine graph that is 90° out of phase with the velocity-time graph
