Final answer:
The Laplace transform of the function 3 sin(5t) is given by 15 / (s^2 + 25), utilizing the formula for the Laplace transform of sin(kt).
Step-by-step explanation:
The student is asking to find the Laplace transform of the expression 3 sin(5t).
The Laplace transform of a function f(t) is a technique used to transform a real-time domain function into a complex frequency domain representation.
It is commonly denoted as L{f(t)}. The Laplace transform of sin(kt) where k is a constant, is given by,
L{sin(kt)} = k / (s^2 + k^2).
Substituting our value of k=5 into the formula, we get the Laplace transform of 3sin(5t) which is 15 / (s^2 + 25).
This transformation is particularly useful in the fields of engineering and physics for the analysis of linear time-invariant systems. The term s represents a complex number in the Laplace transform and is part of the transformed function or the Laplace domain function.