Practice Summary (9.2) - Laplace Transform of Unit Step Function - Mathematics - iii (Differential Calculus) - Vol 1

Practice: Summary

Lesson 9.2Laplace Transform of Unit Step Function

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10 questions

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6 sample questions

Question 1.
What is the value of the unit step function $u(t-2)$ at $t=1$ ?
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Remember that it equals 0 for times less than 'a'.
Question 2.
State the general Laplace Transform formula for the unit step function.
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Think about what parts relate to the shift and the function itself.
3Question 3.
What is the value of the unit step function $u(t-1)$ when $t < 1$ ?
- 0
- 1
- Undefined
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Think back to the definition of the unit step function.
4Question 4.
The Laplace Transform of the unit step function $u(t-a)$ is:
- \$ \\frac{e^{-as}}{s} \$
- \$ \\frac{e^{as}}{s} \$
- \$ \\frac{1}{s} \$
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Use what you've learned about the exponential decay in transformation.
Question 5.
Formulate the Laplace Transform for the function $e^{3t}u(t-2)$ and solve for its inverse.
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Remember to adjust for the value of 'a' in the shifting.
Question 6.
Solve $y'' + 4y = u(t-1)$ using the Laplace transform and find the complete solution.
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Consider the initial conditions you have with this equation.

6 more questions in this section. Enroll free to practise them all.