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Mechanical Engineering QUESTION #2391
Question 1
The Laplace transform of a unit step function \(u(t)\) is:
  • \(\mathcal{L}\{u(t)\} = 1\)
  • \(\mathcal{L}\{u(t)\} = 1/s\)✔️
  • \(\mathcal{L}\{u(t)\} = 1/s^2\)
  • \(\mathcal{L}\{u(t)\} = s\)
Correct Answer Explanation
The Laplace transform of the unit step function: \(\mathcal{L}\{u(t)\}=\int_0^\infty e^{-st}dt=1/s\). The ramp \(tu(t)\) has transform \(1/s^2\); the impulse \(\delta(t)\) has transform 1.