Find attached solution. Note to find the transfer function is relatively straight forward. To then find the specific ...
From a given first order differential equation this is solved using Laplace transform methods going through to find the Laplace domain transfer function, finding the inverse Laplace transform of the delta input transfer function and convolution integral to find the exact solution due to a ramp 4t input. An alternative method to derive the time domain soltuion for the poutput based on partial fraction expansion of the s domain output is also shown
Laplace Transform Method and Control Systems
See the attached document for the full problem set.
4.a) Using the Laplace transform technique, find the transient and steady state response of the system described by the differential equation
(d^2*y)/dt^2) + 3dy/dx + 2y = 1
with initial conditions
y(0^+) and dy | =1
dt | t = 0+