GATE_AE_2027_MOCK_03_Q38
GATE 2027 Aerospace Engineering All-India Master Mock 03 (Flight Dynamics, Controls & Space Trajectories)
NAT · 2 Marks
Engineering Mathematics • Differential Equations • Laplace Transforms & Cauchy-Euler Equations
What is the Laplace transform L{e^{3t} \cos(4t)} evaluated at s = 5? (Round off to three decimal places).
Answer Key:
0.100
Step-by-Step Verified Solution
### Solution: L{e^{at} \cos(bt)} = (s - a) / ((s - a)^2 + b^2). Here a = 3, b = 4. At s = 5: (5 - 3) / ((5 - 3)^2 + 4^2) = 2 / (2^2 + 16) = 2 / (4 + 16) = 2 / 20 = 0.100. Correct: 0.100.