Practice Examples (13.9) - Convolution Theorem - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
What is the convolution of f(t) = t and g(t) = e^{-t}?
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Use integration by parts to solve the integral.
Question 2.
How do we use the Laplace transform in solving differential equations?
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Identify the initial conditions before applying the transform.
3Question 3.
What is the result of the convolution of f(t) = t and g(t) = e^{-t}?
- (t-1) + e^{-t}
- (t+1)e^{-t}
- t^2 + e^{-t}
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Think of the integral representation of convolution.
4Question 4.
True or False: Convolution allows us to convert a differential equation into an algebraic equation.
- True
- False
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Consider the conversion process.
Question 5.
Evaluate the convolution of f(t) = sin(t) and g(t) = cos(t). Provide detailed steps showing the setup and final result.
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Use angles for simplifying the integration.
Question 6.
Solve the differential equation y'' + 2y' + y = e^{-t} using convolution and provide the solution expression.
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Express the right side with the impulse response for simplification.

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