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bliengme

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14 years, 16 days
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These are questions asked by bliengme

ODE second order plot both y and y'...

bliengme 70 Maple
plot ode differential-equation
December 14 2018
1 0

I have modeled a simple pendulum with large intital amplitude (so we do not approx sin(theta) by theta).

I have a plot of theta agains time but would like to have both theta (position) and theta' (velcocity) on same graph.

Grateful for any suggestions

Pendulum2time.mw
 

Simple pendulum without approximating sin(θ) to θ

> 

restart; with(DEtools)
> 

ode := diff(theta(t), t, t)+g*sin(theta(t))/L = 0; ics := theta(0) = 1, (D(theta))(0) = 0

diff(diff(theta(t), t), t)+g*sin(theta(t))/L = 0

  

theta(0) = 1, (D(theta))(0) = 0

 (1)
> 

g := 9.8; L := .75
> 

ans := dsolve({ics, ode}, theta(t), numeric, output = Array([0, .1, .2, .3]))

Matrix(%id = 18446746279246469110)

 (2)
> 

NULL
> 

DEplot(ode, theta(t), t = 0 .. 3.5, theta = -1 .. 1, [{ics}], linecolour = blue)

 
> 

with(plots); odeplot(dsolve({ics, ode}, theta(t), numeric), t = 0 .. 3.5, colour = blue)

 
> 

NULL


 

Download Pendulum2time.mw

 

Using unapply and assign...

bliengme 70 Maple
assign unapply
December 09 2018
1 7

Top part of worksheet gives me a and b; lower part does not

Please tell me where I go wrong. Thanks

Test1.mw

Problem with subs command...

bliengme 70 Maple
substitution subs
November 30 2018
2 6

I know this is a trivial worksheet (in document mode) but why does the second subs fail? Thanks  Gravity.mw
 

``

Justification for using mg as the force exerted by mass m in gravity field g

Using Newton's Law of Gravity, find ``

work := `assuming`([int(G*M*m/r^2, r = R .. R+h)], [0 < R, 0 < h])

G*M*m*h/(R*(R+h))

 (1)

``

R is >> h, so let R + h = R

work := subs(R+h = R, work)

G*M*m*h/R^2

 (2)

``

G, M and R are all constants, so let GM/R² = g

work := subs(G*M/R^2 = g, work)

G*M*m*h/R^2

 (3)

``

``


 

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How to read Help on Eigenvectors...

bliengme 70
2dmath linearalgebra indexing
November 26 2018
1 1

In the snip from Maple help: please expaln (a) the meaning, (b) how do I enter e1..-1,2 in the last statement?

Thanks


Complex roots of exp(x)+sin(x)-2...

bliengme 70 Maple
rootfinding fsolve allvalues
November 19 2018
1 1

Using allvalues (twice) I can uncover the three roots of this expression: 1 real, 2 complex. But fsolve gives me just one real and 1 complex. Interestingly the free version of Woldframalpha.com gives the same single complex root.

Is there any way of coercing fsolve to give both?

Many thanks for any advice

Fsolve5.mw
 

 

Examples of the fsolve command: not all complex roots found

> 

restart
> 

expr := exp(x)+sin(x)-2

exp(x)+sin(x)-2

 (1)
> 

w := solve(expr)

RootOf(_Z-ln(-sin(_Z)+2))

 (2)
> 

w1 := evalf(allvalues(w))

.4486719164

 (3)
> 

w2 := allvalues(w)

RootOf(_Z-ln(-sin(_Z)+2), .4486719164), RootOf(_Z-ln(-sin(_Z)+2), 1.837819685+2.792964964*I), RootOf(_Z-ln(-sin(_Z)+2), -4.707337346-1.315656030*I)

 (4)
> 

q0 := evalf(w2[1])

.4486719164

 (5)
> 

q1 := evalf(w2[2])

1.837819685+2.792964964*I

 (6)
> 

q2 := evalf(w2[3])

-4.707337346-1.315656030*I

 (7)
> 

eval(expr, x = q0); eval(expr, x = q1); eval(expr, x = q2)

0.

  

0.1e-8+0.1e-8*I

  

0.-0.786e-9*I

 (8)
> 

r1 := fsolve(expr)

.4486719164

 (9)
> 

r2 := fsolve(expr, complex)

1.837819685+2.792964964*I

 (10)
> 

NULL
> 

``


 

Download Fsolve5.mw

 

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