spring_sweep_ode

spring_sweep_ode, a MATLAB code which computes a grid of solutions to a parameterized system of ordinary differential equations (ODE) that represent the motion of a spring with mass m, damping b, and stiffness k.

Consider the parameterized second order differential equation:

        m x'' + b x' + k x = 0
      

We now suppose that we are interested in properties of the solution x(t) over the time interval from 0 to 25 seconds, as we vary the physical properties b and k. In particular, we would like to know the maximum value of x(t) over the time interval for each choice of the physical parameters.

To answer this question, we must solve the ODE for each choice of the parameters.

The basic function has the form:

function peakVals = ode_fun ( bVals, kVals )

• bVals is an array of B values;
• kVals is an array of K values;
• peakVals is an array containing the maximum value of the ODE solution for each combination of B and K.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

spring_sweep_ode is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

spring_sweep_ode_test

matlab_ode, MATLAB codes which set up various ordinary differential equations (ODE).

Source Code:

• spring_deriv.m, returns the right hand side of the ODE.
• spring_parameters.m, returns parameters of the ODE.
• spring_peak_display.m, displays a contour plot of the results of the parameter sweep.
• spring_sweep.m, sets up the ODE over a range of parameter values.