Get a parametric solution for z with parameter a:

Evaluating with a numerical value of a gives an approximate function solution for z:

Evaluate at a time t=10:

Plot the solutions for several different values of the parameter:

Get a parametric solution for z with respect to the initial value of y:

Plot the solutions for several different values of the parameter:

Show the sensitivity of the variable z to the parameter a:

The sensitivity with respect to a increases with time:

Optimize parameters for maximizing a throw by a trebuchet:

Retrieve a parametric function for the thrown distance, varying release time and rope length:

Maximize the throwing distance, constraining parameters to reasonable ranges:

Simulate using the optimal throwing parameters:

Show the distance until the first bounce:

Plot the trajectory of the thrown object using a stored plot:

Calibrate parameters in a model by comparing to measurement data:

Compute a parametric function for the inertia variable measured:

Set up a criteria function for model fitting:

Fit parameters to the test data:

Simulate with the fitted parameters:

Show the test data and the calibrated model together:

SystemModelSimulateSensitivity can be used to easily compute parameter sensitivity:

Plot sensitivity bounds for y and z when varying a by 10%: