Math 216
Midterm Exam 2
Winter 2024
Full Name:
uniqname:
ID Number:
Instructions:
1. To receive credit, show all of your work for each problem. Write as neatly as you can if
you want your answers to be read and graded.
2. The last two pages of the exam are tables of antiderivatives and Laplace transforms. You
may detach those pages if you like, but keep all other pages together, and make sure any
work you want graded is not on the detached page.
3. No calculators, phones, smartwatches, Google glasses, etc. No notecards or note sheets.
Closed book.
4. The LSA Community Standards of Academic Integrity are in force. By taking this exam,
you agree to be bound by them. DO NOT CHEAT!
, Problem 1: Consider the following ODE describing the oscillations of a mass on a spring:
x′′+ α x′+ x = β cos(γ t).
Below are graphs of x(t) vs. t for the following six different choices of the parameters (α, β, γ):
1
(1) α =4,β=0,γ =0 (2) α = ,β=0,γ =0
4
11
(3) α =4,β=1,γ =1 (4) α = 0 , β = 1 , γ =
10
1
(5) α = ,β=1,γ =1 (6) α = 0 , β = 1 , γ = 1
10
Write below each graph which case (1 through 6) likely generated that graph:
Case: 1 Case: 5
Case: 6 Case: 4
Case: 2 Case: 3
Midterm Exam 2
Winter 2024
Full Name:
uniqname:
ID Number:
Instructions:
1. To receive credit, show all of your work for each problem. Write as neatly as you can if
you want your answers to be read and graded.
2. The last two pages of the exam are tables of antiderivatives and Laplace transforms. You
may detach those pages if you like, but keep all other pages together, and make sure any
work you want graded is not on the detached page.
3. No calculators, phones, smartwatches, Google glasses, etc. No notecards or note sheets.
Closed book.
4. The LSA Community Standards of Academic Integrity are in force. By taking this exam,
you agree to be bound by them. DO NOT CHEAT!
, Problem 1: Consider the following ODE describing the oscillations of a mass on a spring:
x′′+ α x′+ x = β cos(γ t).
Below are graphs of x(t) vs. t for the following six different choices of the parameters (α, β, γ):
1
(1) α =4,β=0,γ =0 (2) α = ,β=0,γ =0
4
11
(3) α =4,β=1,γ =1 (4) α = 0 , β = 1 , γ =
10
1
(5) α = ,β=1,γ =1 (6) α = 0 , β = 1 , γ = 1
10
Write below each graph which case (1 through 6) likely generated that graph:
Case: 1 Case: 5
Case: 6 Case: 4
Case: 2 Case: 3
