MATH215 December 2011
• Q1 (a) • Q1 (b) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) • Q7 (d) •
Question 05 (c)
Let f and g be two functions satisfying the following conditions
where F(s) and G(s) are the Laplace transforms of the functions f(t) and g(t), respectively. Find the value of g(5).
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
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How can we use the identity
to our advantage?
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From the chart at the end of the exam we have the following identity
and we should always consider this identity first if we see products of polynomials and transforms. Comparing this to what we have,
we see that since and then
Therefore we have
We now need to compute . Returning again to our chart we have the identity
where u_c is the Heaviside function defined as
Using this identity, we can immediately write
Therefore we have that
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MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Laplace transforms