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ES 214
Exam 2 programming portion
January 30, 2026
Rules:
e Theexamis closed-book and closed-notes.
e Personally crafted help sheets are not allowed.
e You may use the provided equation packet. You’re welcome to make any annotations and
notes in this packet.
e Laptops are not allowed.
e You may use your calculator.
e No scratch sheets are allowed. All work must be shown in this exam packet.
Instructions:
e Each problem will be graded as all or nothing. Any justification you provide will not be graded.
e For multiple-choice problems, FILL IN the correct bubble.
e Forshort-answer problems, iven inst s
e When fini i ti et
: Problem Score Problem Score
| 1 /2 5 1
2 /2 6 n
3 Al 7 Al
4 n 8 n
| Total /10
1711
, Problem 1 (2 pts)
We have a DE model in first-order form and its initial conditions as shown.
DE modelin first-order form State variables Initial conditions
d [*1 X2 x =6 6(0) = Orad
dt |x,] 7 |22 (5 — %) ,
X, =6 6(0) = 4rad/s
We numerically integrate this DE model using Euler’s method with time step At = 0.5 s.
Select the correct pair for the values of 8 and 6 attime t = 1.0 s:
6 6 ‘
!
O 7 rad 25rad/s );
O 3rad 5rad/s
O 8rad 20rad/s
O 4 rad 24 rad/s 7
X, ( 14
O 2rad 14 rad/s g
b ( 5]
29
@ 9 rad 35rad/s
O 0 rad 4rad/s
O 6 rad 10rad/s
O 4 rad Orad/s
O 11rad 5rad/s
O None of the above pairs is correct.
2/11
ES 214
Exam 2 programming portion
January 30, 2026
Rules:
e Theexamis closed-book and closed-notes.
e Personally crafted help sheets are not allowed.
e You may use the provided equation packet. You’re welcome to make any annotations and
notes in this packet.
e Laptops are not allowed.
e You may use your calculator.
e No scratch sheets are allowed. All work must be shown in this exam packet.
Instructions:
e Each problem will be graded as all or nothing. Any justification you provide will not be graded.
e For multiple-choice problems, FILL IN the correct bubble.
e Forshort-answer problems, iven inst s
e When fini i ti et
: Problem Score Problem Score
| 1 /2 5 1
2 /2 6 n
3 Al 7 Al
4 n 8 n
| Total /10
1711
, Problem 1 (2 pts)
We have a DE model in first-order form and its initial conditions as shown.
DE modelin first-order form State variables Initial conditions
d [*1 X2 x =6 6(0) = Orad
dt |x,] 7 |22 (5 — %) ,
X, =6 6(0) = 4rad/s
We numerically integrate this DE model using Euler’s method with time step At = 0.5 s.
Select the correct pair for the values of 8 and 6 attime t = 1.0 s:
6 6 ‘
!
O 7 rad 25rad/s );
O 3rad 5rad/s
O 8rad 20rad/s
O 4 rad 24 rad/s 7
X, ( 14
O 2rad 14 rad/s g
b ( 5]
29
@ 9 rad 35rad/s
O 0 rad 4rad/s
O 6 rad 10rad/s
O 4 rad Orad/s
O 11rad 5rad/s
O None of the above pairs is correct.
2/11
