SUMMARY
The Laplace Transform of cos(2at) is derived using the formula L[cos(bt)] = s/(s² + b²). The correct application involves recognizing that cos(2at) can be expressed as 1/2(1 + cos(2at)), leading to L[cos(2at)] = s/(s² + (2a)²). The initial attempt mistakenly omitted the +2at term in the numerator, which is crucial for accurate transformation. The correct Laplace Transform is thus L[cos(2at)] = s/(s² + 4a²).
PREREQUISITES
- Understanding of Laplace Transforms
- Familiarity with trigonometric identities
- Knowledge of basic calculus
- Ability to manipulate algebraic expressions
NEXT STEPS
- Study the properties of Laplace Transforms in detail
- Learn about the inverse Laplace Transform techniques
- Explore applications of Laplace Transforms in differential equations
- Review trigonometric identities and their applications in transforms
USEFUL FOR
Students in engineering or mathematics, particularly those tackling differential equations and Laplace Transforms in their coursework.