# spring_sweep_ode

spring_sweep_ode, a Python 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
```
which represents the behavior of a spring mass system with a mass of m, a spring constant of k and a damping coefficient b.

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 )
where
• 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.