Download MathCAD Homework: Solving Quadratic Equations, Plotting Functions, and Symbolic Algebra - and more Assignments Mechanical Engineering in PDF only on Docsity!
MathCAD Homework
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Basic calculations (solution to quadratic equation: ax
2
a := 1 b := 2 c := 3
x 1
โb b
2
2 aโ
:= x 2
โb b
2
โ โ4 aโ
โ
c
2 aโ
x 1
= โ 1 +1.414i x 2
=โ 1 โ1.414i
checking results:
f x( ) a x
2
:= โ
+ b xโ
+c
f x ( 1 )
= 0 f x ( 2 )
Plotting a function using a range variable
x := โ 5 , โ4.95.. 3 x
-4.
-4.
-4.
-4.
-4.
-4.
-4.
-4.
-4.
-4.
-4.
-4.
-4.
-4.
...
โ 4 โ 2 0 2
0
5
10
15
20
f x( )
x
Using units and significant digit display
m := 100 lbโ
v := 60 mphโ
a 20
ft
sec
2
p := m vโ
p 1.217 10
3
ร
m kgโ
s
F := m aโ
F =62.2 lbfโ
Symbolic Algebra
x
2x โ3 xโ
โ
y
( x โ 2 )
2
(y + 2 )
x y( )
6 yโ
+ โ(y + 2 ) โ
(3 y โ
โ 2 )โ 4
3 yโ
โ 2
โ( y + 2 ) โ
( 3 yโ
โ 2 )โ 6 yโ
+ 4
3 yโ
โ 2
x 5( )
0
= 2 +0.734i x 5( )
1
= 2 โ0.734i
Symbolic Calculus
a := 6.1 redefine "a" to be unitless (see above), so MathCAD is
not confused below.
f x( ) ( x โa)
2 10 sin 2 x(^ โ
)
x
d x( ) 2 xโ
โ 2 aโ
20
cos 2 x( โ
)
x
sin 2 x( โ
)
x
2
x :=โ 5 , โ4.95.. 5
โ 5 0 5
0
50
100
150
f x( )
x
โ 5 0 5
โ 40
โ 20
0
20
d x( )
x
general programming problem example: find the sum of first N numbers divisible by 3
N := 10000
results i โ 0
n โ 0
total โ 0
i โi + 1
remainder โmod i 3( , )
total total i if remainder = 0
0 otherwise
n โ n + 1 ifremainder = 0
whilen <N
( i total)
results 3 10
4
ร 1.5 10
8
ร
= largest results
0 0,
:= largest 3 10
4
= ร
sum results
0 1,
:= sum 1.5 10
8
= ร
alternative solution (for this problem)
i := 3 6, ..3 Nโ
sum
i
i
:= sum 1.5 10
8
= ร
other (even better) alternative solutions (for this problem):
1
N
i
i
8
= ร or^3
Nโ
(N + 1 )
8
= ร
Finding roots
f x( ) 2 x
2
:= โ
โ 4 sin xโ
( )โ 2
x := 1 root f x( ( ) x, ) =1.
x := โ 1 root f x( ( ) x, ) =โ0.
x :=โ 1 , โ0.9.. 2
โ 1 0 1 2
โ 4
โ 2
0
2
4
f x( ) 0
x
marker added at 0
on vertical axis
Solving a set of nonlinear equations
x := 1 y := 1 initial guess
Given
x 2 y
2
= โ
y
sin x( )
x
= +x yโ
solution :=Find x y( , )
x solution
0
:= x = 0.252 y solution
1
:= y =1.
Checking results (solving symbolically and plotting)
y
sin x( )
x
= +x yโ
x 2 y
2
= โ
fb x( )
sin x( )
x โ
(x โ 1 )
fa x( )
โ x โ 2 โ
i
x โ 2 โ
i
fa x( )
0
= 1.322 fb x( ) =1.
x :=0.01 0.05, ..0.
0 0.1 0.2 0.3 0.
1
2
fa x( ) 0
fb x( )
x
Iterative calculations with subscripts
i := 1 .. 10 x
0
:= 1 y
0
x
i
x
i 1โ
y
i
x
i 1โ
x
i
x
0 0 1 2 3 4 5 6 7
1
3
5
7
9
11
13
...
= y
0 0 1 2 3 4 5 6 7
1
2
4
6
8
10
12
...
