Math 234 Practice Exam 2 Key
1.) [10 points] Find the indicated Laplace Transform.
a.) ℒ 4 − 6 − 14
b.)
ℒ 3 cos2 − 42
c.)
ℒ sin3 ∗ cosh5
d.)
ℒ sin3
e.)
ℒ cos4 − 1
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2.) [10 points] Find the indicated Inverse Laplace Transform. Do not use convolutions.
a.) ℒ − "
+ 7 ! &
!
! #
b.)
ℒ c.)
ℒ d.)
ℒ !
! !'
( )*+
!" '#
!
&
!" ',!'
&
&
2
3.) [10 points] Charizard performed the calculations shown below.
Explain what is wrong with Charizard's calculation and then show the
correct way to do the problem.
a.) Compute ℒ sin4.
ℒ sin4 - ℒ ℒsin4 - .
1
4
4
0. 0 -
/ − 3/ + 16
/ − 3 / + 16
Laplace Transforms do not break up under products: ℒ12 3 ℒ1ℒ2.
This property only works for convolutions: ℒ1 ∗ 2 - ℒ1ℒ2.
Use Rule 19 with a=3, b=4:
!( )4+
b.) Compute ℒ "
&.
! ℒ ,!
!
!
& - − 6ℒ !"& - − 6 cosh5
! " Rule 27 says we have to shift the function 1 to 1 − 6.
3
4.) [20 points] Solve the initial value problem:
5 66 − 25 6 − 35 - 4 − 2,
50 - 2,5 6 0 - 0