Engineering Mathematics (I) – Homework 6
不需繳交，自行練習
Question 1: Find the Laplace transforms of the following functions.
(a)
(b)
e2t cosh t
cos(t   )
(c)
Question 2: Find the inverse Laplace transforms of the following
functions.
(a)
(b)
(c)
(d)
(e)
s 4  3s 2  12
s5
n L
2 2
L s  n 2 2
1
1

2
s 5 s5
15
s 2  4s  29
1
s2  s
2
Question 3: Solve the initial value problem by the Laplace transform.
(a)
(b)
(c)
(d)
(e)
1
y'  y  17sin 2t,
2
y(0) = -1
y''  2y'  2y  0,
y(0)=1,
y''  7y'  12y  21e3t ,
y(0)=3.5,
y''  3y'  2.25y  9t 3  64,
y''  3y'  4y  6e2t 2 ,
y(0)=1,
y(1)=4,
y ' (0) = -3
y' (0) = -10
y' (0) = 31.5
y ' (1) = 5
(f)
y''  y  r(t),
 t if 0<t<1
r(t)= 
;
0 if t>1
y(0)=y ' (0)  0.
Question 4: Sketch the given function (which is assumed to be zero
outside the given interval). Represent it using unit step functions.
Find its transform.
(a)
(b)
(c)
t2
(1<t<2)
cos  t
(1<t<4)
t
(5<t<10)
Question 5: Find f(t), if F(s) equals:
(g)
(h)
e 4s
s2
se 3s
s2  4
Question 6: Using the Laplace transform and showing the details,
find the current i(t) in the circuit in Figure, assuming i(0)=0 and