Question

Find the Laplace transform of the periodic function whose graph is given below.

$1473c8bf-86b7-3406-9309-475b519ebf71___4$
(Click on graph to enlarge)

$\displaystyle F(s) = {\mathcal L}\left\lbrace f(t) \right\rbrace =$ ________ $\displaystyle \cdot \Bigg( \int_0^2$ ______    $\displaystyle + \int_2^4$ ______    $\displaystyle + \int_4^5$ _________$\displaystyle \Bigg)$ = _________

Answer 1

"We know the following theorem: Theorem suppose that f: [0, infinity) rightarrow R is a periodic function of period T > 0, ie, f(x + T) = f(x) forall t greaterthanorequalto 0. If the Laplace transform of f exists, then F(s) = 1/1 - e^- 8t integral^T_0 f(t) e^- st dt From the graph of the given function, we can say the f is a piecewise continuous function on the interval [0, 5] and also,