Final answer:
To find the Laplace transformation of the function (2t+1)² +cos(3t+π/3), apply the properties and formulas of Laplace transforms.
Step-by-step explanation:
The Laplace transformation of the function (2t+1)² +cos(3t+π/3) can be found by applying the properties and formulas of Laplace transforms. Here is the step-by-step process:
- Apply the linearity property to separate the Laplace transform of each term: L{2t+1}² + L{cos(3t+π/3)}
- Use the power rule: L{2t+1}² = (2/s)² + 2/s + 1/s
- Use the trigonometric identity: L{cos(3t+π/3)} = s/(s²+3²) + π/(s²+3²)
- Simplify and combine the terms to get the final Laplace transform expression
By following these steps, you can find the Laplace transformation of the given function.