Question

Please answer all questions and Please Write Clearly

Problem #1 : (14%) Consider the following differential equation: 0.2' dc(t) + x(t)-21,(t) with initial condition x(0)=1 and u (1) being a unit step function. dt la) Convert the differential equation into a Laplace transformed algebraic equation in which X'(s) is the Laplace transform of x(t). (3%) (lb) Solve the algebraic equation for X(s). (3%) (1 c) Find the inverse laplace transform of x(s) , which is the solution of the differential equation x(t). (4%) Sketch the output response x(t) and specify the initial value, final value, the time constant τ, and the value of x(t) at t = τ . (4%)

Answer 1

2-t '1s US5) S (StS) -5t (ST5 S-t5 le) 2-e-st- プ) e_ st_ 2-1,26仁.}. → O'632 x2: 1264 26y