***IN MATLAB*** ***Just Solve Problem 2***

Problem 1

a) The motion of a given vehicle can be modeled by the ordinary differential equation . Analytically convert this ordinary differential equation into an equivalent system of coupled first order ordinary differential equations. b) A particular spring-mass system can be modeled by the coupled ordinary differential equations . Analytically convert this coupled ordinary differential equation system into an equivalent system of coupled first order ordinary differential equations.

Problem 2

Use ode45 and one other solver of your choice to numerically solve the systems in Problem 1, and plot your states vs. time. Supply your own initial conditions, time steps, and time intervals. Experiment with how the results change based on varying these inputs, and comment on your observations in a statement that prints to the Command Window. In the case of Problem 1(a), since this is a second order ordinary differential equation, you will need to specify two initial conditions: and . In the case of Problem 1(b), since this is a coupled system of second order ordinary differential equations, you will need to specify four initial conditions: , , , and . Use a value of 10 N/m for , 5 N/m for , 15 kg for , and 12 kg for .