In each of Problems 14 through 21 , express the total response of the given initial value problem using a convolution integral to represent the forced response: y ' ' + ω 2 y = g ( t ) ; y ( 0 ) = 0 , y ' ( 0 ) = 1
In each of Problems 14 through 21 , express the total response of the given initial value problem using a convolution integral to represent the forced response: y ' ' + ω 2 y = g ( t ) ; y ( 0 ) = 0 , y ' ( 0 ) = 1
In each of Problems
14
through
21
, express the total response of the given initial value problem using a convolution integral to represent the forced response:
y
'
'
+
ω
2
y
=
g
(
t
)
;
y
(
0
)
=
0
,
y
'
(
0
)
=
1
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Q3*) Consider the integral
I
Yn, Y₁, Y2, . . ., Y'n) dã,
[F(x, Y 1, Y2, · · Yng)
= -
where y1, 2, ...y are dependent variables, dependent on x. If F is not explicitly dependent on x, deduce
the equivalent of the Beltrami identity. Optional: Give an example of a function F(y1, Y2, Y₁, y2), and write
down the Euler-Lagrange equations and Beltrami Identity for your example. Does having this Beltrami Identity
help solve the problem?
Write an integral that is approximated by the following Riemann sum. Substitute a
into the Riemann sum below where a is the last non-zero digit of your banner ID.
You do not need to evaluate the integral.
2000
(10
1
((10-a) +0.001) (0.001)
Solve the following problem over the interval from x=0 to 1 using a step
size of 0.25 where y(0)= 1.
dy
=
dt
(1+4t)√√y
(a) Euler's method. (b) Heun's method
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