Mathematics > EXAM > MATH 225 Midterm #2, Individual Test - Solutions Worked out. Graded A (All)

MATH 225 Midterm #2, Individual Test - Solutions Worked out. Graded A

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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. [Show More]

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