Practice Steps For Solving Odes Using Laplace Transform (184) - Application to Ordinary Differential Equations (ODEs)

Practice: Steps for Solving ODEs using Laplace Transform

Lesson 184Application 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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6 sample questions

Question 1.
What is the first step in solving an ODE using the Laplace Transform?
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Think about what the definition of the Laplace transform is.
Question 2.
What does Y(s) represent in this context?
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Recall what happens to functions when transformed.
3Question 3.
What is the role of the Laplace Transform in solving ODEs?
- Transforms ODEs to algebraic equations
- Eliminates initial conditions
- Directly solves ODEs
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Consider why we might choose to transform an equation.
4Question 4.
True or False: Initial conditions can be directly included in the Laplace Transform.
- True
- False
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Think about how the initial values affect the behavior of the solution.
Question 5.
Given the ODE d2y/dt^2 + 5dy/dt + 6y = cos(t) with y(0) = 1, y'(0) = 0, solve for y(t).
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Be mindful of correctly applying the cos(t) transform.
Question 6.
Solve the differential equation for a damped harmonic oscillator: d2y/dt^2 + 2ζω_n dy/dt + ω_n^2y = sin(ωt) where y(0) = 0, y'(0) = 0.
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Identify which frequency response functions apply here!

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