I've tried to obtain the the steady state output with the help of final value theorem and multiplication properties of Laplace transform.But I'm not sure whether I've solved the problem correctly or not. Please let me know if any corrections are required.

This is the question.

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This is the approach I've tried. The solution is 45. But I'm not sure whether I've made the correct assumption of input signal x(t) as a step signal with amplitude 5. enter image description here


1 Answer 1


Yes, for these Laplace transform problems, "constant input" translates to "unit step".

As a further check, you can reason through it -- while convolution is usually not something to try to do in your head, the convolution of a pulse with a constant is just the height of the pulse times the constant, integrated over the duration of the pulse. So, 3 * 3 * 5 = 45, which is not only the answer you got, but which follows the arithmetic in your final few lines fairly closely.

(BTW: If I were a grad student grading your work you would have gotten full marks.)

  • \$\begingroup\$ Hey Tim, thanks for the clarification and your kind words.. :) \$\endgroup\$
    – Karthik
    Commented Sep 13, 2019 at 20:13

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