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Consider the following initial value problem, in which an input of large amplitude and short duration...

Question:

Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a

Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" – 2x' = (t – 4), x(0) = 4, x'(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution z(t). x(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. if 0 <t<4, x(t) = if 4 <t< 0. Instructions

Answers

x 2.3 s (mm) 200)=*, X6)=0. 15x] -21[x] = [5 (44] $22[%] - 5.40) – s0) –> (32[x] – xc0)]- stes (52_25) 15x] - HS-0 +2.4 eus

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