Simple Harmonic Motion Flashcards
What is acceleration in terms of angular frequency and displacement?
a=-kx where k is angular frequency squared, w^2 which is equal to (2pifrequency)^2.
If displacement produces a cos graph, where x=Acos2pift, what will the velocity and acceleration graphs look like?
Velocity graph is a negative sine wave, a sinusoidal graph, with equation -2pifAsin(2pift)
Acceleration graph is further differentiated to give a negative cos graph, (-4pi^2f^2Acos(2pift)
A = amplitude, f= frequency, t=time.
When a block of mass m is pulled to the right on a coil, what will happen?
There is a larger resultant force, F=-kx, to its left, which has more extension. The mass will therefore accelerate to the other side, and as the net force reaches zero, displacement also becomes zero. As the velocity decreases, with the net force accumulating now on the right side as this becomes more extended than the left coil side, displacement from equilibrium will become negative as the force increases and becomes positive.
The force curves in an S shape from negative to positive, velocity is a negative U shape starting from 0 and finishing at 0, and displacement curve is a S shape from positive to negative.
What trend must hold for simple harmonic motion/oscillation?
Acceleration is proportional to negative displacement with a straight line graph.
What is the equation for acceleration of a mass on a spring?
a=-kx/m which is equal to the displacement differentiated twice.
What is the iterative process for determining acceleration, change in velocity, new velocity, change in displacement, and new extension?
When this process is used to draw an x-t graph, what are limitations?
a=-kx/m where k is spring constant, dV=a*dt, Vnew=Vold+dV, dX=Vnew+Vold/2 *t, Xnew=x+dX.
Displacement against time produces a sinusoidal wave but displacement is initially held as constant which isn’t accurate. Alongside this, as time increases, the amplitude is found to rise, which doesn’t occur in SHM.
What did Galileo observe about time periods?
Galileo observed that pendulums have a constant time period no matter the size.
Define time period, equilibrium, and amplitude.
Time period = time for one swing of pendulum
Equilibrium = zero displacement and no net force
Amplitude = greatest displacement
What are time periods defined as, and how does displacement vary, for SHM?
Time periods for SHM are isochronous, same time, and displacements vary sinusoidally.
What is the formula for angular frequency?
Angular frequency = 2pif.
What defines if motion is SHM?
Restoring force pulls an oscillator back to equilibrium. SHM is shown if:
Acceleration proportional to negative displacement.
Acceleration directed towards equilibrium
