question archive Find the total solution to the differential equation:(D^3 + 5D^2 + 12D + 15)y(t) = (D + 0
Find the total solution to the differential equation:(D^3 + 5D^2 + 12D + 15)y(t) = (D + 0
Subject:Electrical EngineeringPrice: Bought3
Find the total solution to the differential equation:(D^3 + 5D^2 + 12D + 15)y(t) = (D + 0.5)f(t)
with initial conditions y(0) = 3, y'(0) = 2, y"(0) = 1 and f(t) = sin(3*pi*t)u(t). Use T = 0.001, and let 0 < = t <= 10.
(a) Using paper-and-pencil analysis, find the impulse response of the system h(t). Then compute and plot its sampled values h[k] = h(kT).
You may use Laplace transform methods if you want. You may also use MATLAB to find the poles.
(b) Find the sampled values of the input function f[k] = f(kT). Plot these values.
(c) The zero-state solution is the scaled convolution T(f[k] * h[k]).
(d) Compute numerically and plot the total solution.
(e) Find an analytical solution to the differential equation and plot it.
(f) Compare the analytical and the numerical solution.
