Question

Given a second-order ordinary differential equation: frac{d^2f(t)}{dt^2} + 4frac{df(t)}{dt} + 3f(t) = r(t) (1) with the following initial conditions: f(0) = 1 and frac{df(0)}{dt} = 0. a) Express Equation (1) in state-space form. Clearly write down the A, B, C, and D matrices. Then find the state transition matrix and determine the solution for f(t) given that the input function r(t) is a unit step function. b) Write a MATLAB-Simulink program to find the computational solution for f(t) in Equation (1) with the input function r(t) given as a unit step function. Compare the analytical solution for f(t) from part (a) and the computational solution for f(t) from part (b) by plotting them together.

          Given a second-order ordinary differential equation:
frac{d^2f(t)}{dt^2} + 4frac{df(t)}{dt} + 3f(t) = r(t) (1)
with the following initial conditions: f(0) = 1 and frac{df(0)}{dt} = 0.
a) Express Equation (1) in state-space form. Clearly write down the A, B, C, and D matrices. Then find the state transition matrix and determine the solution for f(t) given that the input function r(t) is a unit step function.
b) Write a MATLAB-Simulink program to find the computational solution for f(t) in Equation (1) with the input function r(t) given as a unit step function. Compare the analytical solution for f(t) from part (a) and the computational solution for f(t) from part (b) by plotting them together.

$Given a second-order ordinary differential equation: fracd^2f(t)dt^2 + 4fracdf(t)dt + 3f(t) = r(t) (1) with the following initial conditions: f(0) = 1 and fracdf(0)dt = 0. a) Express Equation (1) in state-space form. Clearly write down the A, B, C, and D matrices. Then find the state transition matrix and determine the solution for f(t) given that the input function r(t) is a unit step function. b) Write a MATLAB-Simulink program to find the computational solution for f(t) in Equation (1) with the input function r(t) given as a unit step function. Compare the analytical solution for f(t) from part (a) and the computational solution for f(t) from part (b) by plotting them together.$

Added by Sarah R.

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