Coshat = s 2
+a 2
s
​
SSCE 1793 ESTION 3 (15 MARKS) sinhat= s 2
+a 2
s
​
Find the Laplace transform of f(t)=tcosh2tsinh3t. 1{f(t)}=1{tcosh2t}⋅{sinh3t}. (4 marks )f(t)= Consider the piecewise function { s 2
s 2
+3 2
​
. Express the function f(t) in terms of unit step function. Then, find the Laplace transform of f(t). (6 marks ) c) Use convolution theorem to find L −1
{F(s)G(s)}=∫ 0
t
​
f(ω)g(t−4)L −1
{ s 2
(s 2
+9)
4
​
}. (5 marks)