Question

The total period of the function shown in the figure is 4 sec and the amplitude is 10. Find the function f1 (t) from t = 0 to 1 in terms of unit step function.

(a) 10t [u (t) – u (t + 1)]

(b) 10t [u (t) + u (t – 1)]

(c) 10t [u (t) + u (t + 1)]

(d) 10t [u (t) – u (t – 1)]

I got this question in final exam.

I'd like to ask this question from Definition of the Laplace Transform topic in portion Intoduction to the Laplace Transform of Network Theory

Answer 1

Correct choice is (d) 10t [u (t) – u (t – 1)]

The best explanation: The function shown in the figure is made up of linear segments with break points at 0, 1, 3 and 4 seconds. From the graph, f1 (t) = 10t for  0 < t < 1. In terms of unit step function, f1 (t) = 10t [u (t) – u (t – 1)].