### Thin Plate Convergence Rate

Raw Data

Methodology:

Three sets of time step sizes are chosen: the step size being 1/200th of the

period of driving force; 1/2000th of the period of the driving force, and

1/20000th of the period of the driving force.

The plate is driven to a stable cyclical state in one frequency first, and

the driving force is switched to a different frequency, and the response and

convergence is then observed as the plate settles into the second frequency.

Files under the directory covergenceTrend_stepsize_1_[200|2000|20000]th_Period/

are results taken from the step sizes being 1/[200|2000|20000]th of the

period of the driving force. The file convergencePlot[x]to[y] shows the

timestep taken Vs response Vs convergence as the driving force's requency is

switched from x to y.

Explanation of terms:

A window is a history of the total energy of the plate

during a past length of time. The length of time is chosen

to be the period of the driving force.

A response is the highest element in the window.

The convergence is the two-norm of the difference

between the FFT coefficient vector obtained using the

current window and the FFT coefficient vector obtained

using some earlier window.

Summary of results:

The response (not convergence) of a given frequency stabilises after

a certain amount of simulated time. It turned out to be about the same

for all frequencies (around 22 units of simulated time.)

The size of a timestep doesn't affect the value of the response, as

long as it is greater than 1/100th of the period of the driving force.

However, taking a timestep size that is larger than 1/40,000th of the

period of the driving force makes the window curve look like a noisy

sine wave, therefore the convergence does not settle down.

Finally, it doesn't matter what the previous configuration of the

plate was in: it takes roughly the same amount of simulated time for

a plate to settle down in to the new configuration.