Practice Application To Ordinary Differential Equations (odes) (18.1) - Application to Ordinary Differential Equations (ODEs)

Practice: Application to Ordinary Differential Equations (ODEs)

Lesson 18.1Application to Ordinary Differential Equations (ODEs)

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What does the Laplace Transform do?
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Think about the relationship between derivatives and algebra.
Question 2.
How is the initial condition represented in Laplace Transforms?
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Look for the term f(0) in derivative transformations.
3Question 3.
What is the first step in using Laplace Transforms to solve ODEs?
- Take the inverse transform
- Substitute initial conditions
- Take the Laplace transform of both sides
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It's all about moving to the s-domain first.
4Question 4.
True or False: Laplace Transforms convert time-domain functions into frequency-domain functions.
- True
- False
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Think about what s represents.
Question 5.
Solve the third-order ODE: d^3y/dt^3 + 5d^2y/dt^2 + 6dy/dt = e^{-t}, with appropriate initial conditions.
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Focus on breaking down the steps and applying partial fractions where needed.
Question 6.
An RLC circuit described by L(d^2i/dt^2) + R(di/dt) + Ci = V(t) is given. Solve for i(t) assuming V(t) is a step input.
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Utilize the known transforms of step functions and derive appropriately.

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