What is the Laplace transform of #tcost# into the #s# domain?

1 Answer
Truong-Son N.
Oct 20, 2016

A Laplace transform converts a function of #t#, #f(t)#, into a new function of #s#, #F(s)#. We denote that as:

#ℒ[f(t)] = F(s)#

where the actual transform can be acquired from a table of Laplace transforms.

For #f(t) = tcos(at)#:

#ℒ[f(t)] = ℒ[tcos(at)] = (s^2 - a^2)/(s^2+a^2)^2#

Therefore, for your function, plug in #a = 1# to get:

#ℒ[f(t)] = ℒ[tcost] = (s^2 - 1^2)/(s^2+1^2)^2#

#= color(blue)((s^2 - 1)/(s^2 + 1)^2)#

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