Revision Test 18
This Revision Test covers the material contained in Chapters 61 to 65.The marks for each question are shown in
brackets at the end of each question.
- Find the Laplace transforms of the following
functions:
(a) 2t^3 − 4 t+5 (b) 3e−^2 t−4sin2t
(c) 3cosh2t (d) 2t^4 e−^3 t
(e) 5e^2 tcos3t (f) 2e^3 tsinh4t (16) - Find the inverse Laplace transforms of the follow-
ing functions:
(a)
5
2 s+ 1
(b)
12
s^5
(c)
4 s
s^2 + 9
(d)
5
s^2 − 9
(e)
3
(s+ 2 )^4
(f)
s− 4
s^2 − 8 s− 20
(g)
8
s^2 − 4 s+ 3
(17)
- Use partial fractions to determine the following:
(a) L−^1
{
5 s− 1
s^2 −s− 2
}
(b) L−^1
{
2 s^2 + 11 s− 9
s(s− 1 )(s+ 3 )
}
(c) L−^1
{
13 −s^2
s(s^2 + 4 s+ 13 )
}
(24)
- In a galvanometer the deflectionθ satisfies the
differential equation:
d^2 θ
dt^2
+ 2
dθ
dt
+θ= 4
Use Laplace transforms to solve the equation forθ
given that whent=0,θ=0and
dθ
dt
=0. (13)
- Solve the following pair of simultaneous differen-
tial equations:
3
dx
dt
= 3 x+ 2 y
2
dy
dt
+ 3 x= 6 y
given that whent=0,x=1andy=3. (20)
- Determine the poles and zeros for the transfer func-
tion:F(s)=
(s+ 2 )(s− 3 )
(s+ 3 )(s^2 + 2 s+ 5 )
and plot them on
a pole-zero diagram. (10)