Question

Using tables of Laplace Transforms and operational theorems, determine

i) L [ 5 sin(3t) + 8H(t-π) cos(t) ]
ii) L [ H(t-8) sin(6t - 48)e⁷ᵗ ]

Answer 1

The question is about finding the Laplace Transform of two given functions using tables of Laplace Transforms and operational theorems, requiring knowledge of properties like the Heaviside step function and translation theorem.

Step-by-step explanation:

The subject of the question is Laplace Transforms, a mathematical tool used in engineering and physics to convert differential equations into algebraic equations. The question pertains to finding the Laplace Transform of two functions:

1. L [ 5 sin(3t) + 8H(t-π) cos(t) ]
2. L [ H(t-8) sin(6t - 48)e⁷ᵗ ]

To solve these, we use the table of Laplace Transforms and the properties of the Laplace Transform. The Heaviside step function, denoted by H(t-a), represents a shift in the function and the translation theorem of Laplace Transforms can be applied. For the second function, we must use the modulation, time-shifting, and possibly other operational theorems to find the transform.