UN IVERS fTY O F BR ITI SH CO LU MB IA
IRVING K. &AftBER SCHOOL
Instructor: Rebecca Tyson Course: MATH 225
Date: Mar 14th, 2018 Time: 11:30am Duration: 35 minutes. ThiB exarli haa 4 questions for a tot
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UN IVERS fTY O F BR ITI SH CO LU MB IA
IRVING K. &AftBER SCHOOL
Instructor: Rebecca Tyson Course: MATH 225
Date: Mar 14th, 2018 Time: 11:30am Duration: 35 minutes. ThiB exarli haa 4 questions for a total of 32 points.
SPECIALINSTRUCTIONS
• Show and explain all of your work unleas the question directs otherwise. Simplify all answers.
• The uae of a calculator is not permitted.
• Answer the questions in the spacea provided on the question sheets. If you run out of room for an anewer, ask for extra paper.
This is a two-stage exam. You have 35 minutes to complete the exam individually, then you will hand in the testa and join your group to redo the test aa a group in the remaining 35 minutes.
Question: 1 2 3 4 Total
Points: 4 5 8 15 32
Score:
This exam consists of 5 menu includine this cover sae . Cheeb to ensure that it is complete
https://www.coursehero.com/file/38888058/MATH-225-Midterm-2-Individual-Test-Solutionspdf/
Path 225 (ktar 14th, 2018) Midterin J2, Individual Test
1. The di8erential equation y" + p = 0 has the general solution y(I) = • cos(t) + ct sin(I) Determine the form of the particular solution for the differential equation below (DO NOT SOLVE!):
p” + y = te" cos(t) — 4sin(t)
2. Consider the IVP
dy - y(2 — z) -I- *, //(0) 1.
(a) Write out the ODE using the Backward Euler and Forward Euler formulae (do not aolve for pq+,).
(b) Your friend chooses to obtain the solution using a di8erent numerical method. After one step of eize h = 0.1, the magpitude of the local error is 0.001. What can you say about the method your friend is using? How does it compare to the Backward Euler method?
Page 2 of 5
Math 225 (Mar 14th, 2018) Midterm @2, Individual Test
3. Consider the maaa-spring system with masa 2 kg, damping coefficieut 1 kg/s, and spring constant 5/4 N/In, Let z(I) represent the displacement of the inass as a function of time.
(a) Write down the differential equation for s(t) when the system is subject to the
forcing /(I) = cos(3t/4).
(b) Given that the solution to the homogeneous system is
z(/) e •"
what is the angular frequency of the homogeneous system?
(c) The general solution of the forced system is
z(/) = Ae' " 2 " sin
+ é +
8 sin + a (1)
i, Explain what the two terms in (1) represent.
ii. What ia the frequency gain of the forced system? How does it compare to the amplitude of the forcing itself? Explain.
• Path 225 (ktar t4th, 2018) Midterm J2, Individual Test
4. Solve the initial value problem
’w“ —2tr’ + tu - e° In(s), s > 0, tu(1) e, to’(1) —e.
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