Examples ex 1. find i) l{tsinkt} ii) l{ tcoskt ) solution : i) let f) = sinkt k l{fo} = l (sinkt) =2 by theoxm (1.9.1) l{tfo) (-1)' f'(s) s2 +k2 f(s) d k l{tsin

EXAMPLES Ex 1. Find i) L{tsinkt} ii) L{ tcoskt ) Solution : i) Let F) = sinkt k L{FO} = L (sinkt) =2 By Theoxm (1.9.1) L{tFO) (-1)' f'(s) s2 +k2 f(s) d k L{tsin kt} = ds s+k2 = 2ks (s+k i) F() = coskt L {FO) = L {coskt) = +k - =f(s) . L{tPcoskt} = L{fF(0} = -13 f(s) d2 ds? s+k