ME375, Fall 2026
Ch 2 Homework problems due Thurs Sept 10:
(1)
State whether each differential equation is linear or nonlinear, and give the reason:
a) y ÿ +5 ẏ=0
b) ẏ+sin y=0
ẏ+ √y=0
2
d) ÿ+5 t ẏ+3 y=0
t
e) ÿ+e y=0
2
f) ÿ+3 t sin y=0
c)
For each of the following, give (a) complete response x(t ) , (b) the free response, (c) the
forced response:
ẍ +14 ẋ+49 x=5 us (t) , with x (0)=−1, ẋ (0)=−3
(2)
(3)
ẍ +5 ẋ +4 x=2 us (t) , with x (0)=2, ẋ(0)=−3
(4)
ẍ +6 ẋ+34 x=68u s (t ) , with x (0)=5, ẋ (0)=7
x (t ) and y (t ) together, where:
ẋ=−2 x+5 y , x (0)=5
ẏ=−6 y−4 x +10 us (t ) , y (0)=2
(5)
Solve for
(6)
Give ζ , τ , ω n , and ω d for the following transfer functions:
5 s +3
2
(a) T (s )=
(b) T (s )= 2
2
10 s +5 s+50
2 s + s+100
(7)
Find the inverse Laplace transform for the following using Matlab:
3 s+2
X (s)= 2
(a)
s ( s+10)
4 s +3
X (s)= 2
(b)
s(s +6 s+34 )
8 s+ 5
X (s)= 2
(c)
2 s + 20 s+ 48
4 s+ 13
X (s)= 2
(d)
s +8 s+116
(8)
Use Matlab to plot the following:
(a) Unit impulse response for 3 ẍ +21 ẋ+30 x=f (t )
5 ẍ +20 ẋ +65 x=f (t )
(c) Response of 4 ẍ +32 ẋ +60 x=f (t) with f (t )=5 t +6 cos 3 t for 0≤t ≤6
(b) Unit step response for