Exam 3 Math 2306 sec. 54 Fall 2021 Name: (4 pts) Your signature (required) confirms that you agree to practice academic honesty. Signature: Problem Points 1 2 3 4 5 6 Total (+4) 1 1 INSTRUCTIONS: There are 6 problems worth 16 points each. You may use one sheet (8.5” × 11”) of your own prepared notes/formulas. No use of a calculator, text book, smart device, or other resource is permitted. Illicit use of any additional resource will result in a grade of zero on this exam as well as a formal allegation of academic misconduct. Show all of your work on the paper provided to receive full credit. 1. Evaluate each Laplace transform. (a) L {e 3t + 3 cos(7t)} (b) L {(2 + t 2 ) 2 } (c) L {2 sin(3t) cos(3t)}
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Exam 3 Math 2306 sec. 54Fall 2021
Name: (4 pts)
Your signature (required) confirms that you agree to practice academic honesty.
Signature:
Problem Points123456
Total (+4)1
1
INSTRUCTIONS: There are 6 problemsworth 16 points each. You may use onesheet (8.5” × 11”) of your own preparednotes/formulas.No use of a calculator, text book, smartdevice, or other resource is permitted.Illicit use of any additional resource willresult in a grade of zero on this exam aswell as a formal allegation of academicmisconduct.
Show all of your work on the paper providedto receive full credit.
1. Evaluate each Laplace transform.
(a) L {e3t + 3 cos(7t)}
(b) L {(2 + t2)2}
(c) L {2 sin(3t) cos(3t)}
2. Find the steady state charge, qp, on the capacitor in the LRC series circuit described by thegiven equation.
q′′ + 2q′ + 5q = 10 sin t
(Note: The transient charge is qc = c1e−t cos(2t) + c2e
−t sin(2t).)
3. Evaluate each inverse Laplace transform.
(a) L −1{
3s
s2 + 16
}
(b) L −1{
1
s9
}
(c) L −1{
s
(s− 1)(s+ 3)
}
4. Suppose that f is defined on [0,∞) and L {f(t)} = 1√s2 + 9
. Evaluate
(a) L {e2tf(t)}
(b) L {f(t− π)U (t− π)}
5. A 3 kg mass is attached to a spring with spring constant 27 N/m.
(a) If there is no damper, and a driving force f(t) = sin(γt) is applied, what value of γ willresult in pure resonance?
(b) If there is no driver, but a dashpot is added to induce damping of β N per m/sec of velocity,what value of β will result in critical damping?