Aerospace Engineering 3515: System Dynamics
Prof. Eric Feron
Midterm examination∗–
I certify that, in full accord with the Honor Code of the Georgia Institute of
Technology, I have neither received assistance from nor given assistance to
other students in taking this examination.
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Last Name (please print):
∗
The exam is closed book. Please turn in the test along with your papers.
Make sure your name is on every sheet that you turn in! Do not write on the
back of any sheet you turn in!
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Problem 1 [10pt]
Find the Laplace transform of f , with
f (t) = 0
f (t) = t2 sin ωt
2
t<0
t≥0
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Problem 2 [10pt]
Find the initial value of df (t)/dt, where the Laplace transform of f (t) is given
by
2s + 1
.
F (s) = L[f (t)] = 2
s +s+1
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Problem 3 [10pt]
Consider the spring-loaded pendulum system shown in Fig. 1. Assume that
the spring force acting on the pendulum is zero when the pendulum is vertical
(θ = 0). Assume also that the involved friction is negligible and the angle of
oscillation, θ, is small. Write the equations of motion for the system.
l
k
k
θ
mg
Figure 1: Spring-pendulum system
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a
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Problem 4 [10pt]
Find the transfer function Y (s)/U (s) of the system shown in Fig. 2. The
vertical motion u at the point P is the input. Assume that the displacements x and y are measured from their respective equilibrium positions in
the absence of the input u.
m2
k2
b
y
m1
k1
x
u
Figure 2: mass-spring-dashpot system
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Problem 5 [10pt]
Consider the system defined by
y 000 + 6y 00 + 11y 0 + 6y = 6u.
Give two distinct state-space representations of the system.
Hint: one of the solutions to the equation
x3 + 6x2 + 11x + 6 = 0
is x = −1.
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