hello, everyone,
the attached pdf file contain four models, I can't get the solutions of last three models.
help, thank you in advance.

123.pdf

The damped driven pendulum is modeled using :

d²(x)/d(t²) + b*d(x)/d(t) + sin(x) = F*cos(x).  (4)

Numerically simulate (4) with b=0.22 and F=2.7

a) Starting from any reasonable initial condition, perform a phase portrait analysis. Show that the time series has an erratic appearance, and interpret it in terms of the pendulum's motion.

b) Plot the Poincare section by sampling the system whenever  t=2*pi*k, where k is an integer.

 d^2(x)/d(t^2) + sin(x)=0  (1)

d^2(x)/d(t^2) + x = 0 (2)

d^2(x)/d(t^2) + ( x - (x)^3/6) = 0 (3)

1) Compare the results of numerical simulations of (1), (2), (3) to see how closely the period of the periodic orbits relate.

a) Perform a phase portrait ( (x)'(t) vs. x ) analysis for (1), (2), and (3).

b) Consider the initial conditions x(0)= x₀ and x'(0)=0. For what intervals of x₀ do the periodic orbits of (2...

Hi there,

can Maple simplify expression

x[1]+x[2]+x[3]+x[4]+x[5]

to

sum(x[i],i=1..5) ?

Or

cos(y[1])+cos(y[2])+cos(y[3])+cos(y[4])+cos(y[5])

to

sum(cos(y[i]),i=1..5)

Its hard to find every such sequences in big equation, so Maple can help may be.

Maple 17 adds several new visualizations in Graph Theory as well as updates to inequality plotting and visualizing branch cuts in mathematical expressions.  In preparing the “what’s new” pages for Maple 17, we decided to showcase several of these plots alongside some of our other favourites.

The following file contains code to create most of the “what’s new” plots, as well as some quick tips and techniques for using the ColorTools package to enhance your plots:...

Hi everybody. Firstly, i apologize for my poor level of english. I am a new maple user and i want to solve the following system, but I face some difficulties. I go through forum, FAQ, courses notes on the net and so on but I don't find the solution. 

I first define the folowing equations:

Hi,

I'm using the DirectSearch package in a 10 periods model and in the first period i get this values:

"

> DirectSearch[SolveEquations](sys, assume = positive);
Warning, complex or non-numeric value encountered; trying to find a feasible point
        [HFloat(1.1842542076623546e-32), 

          Vector[column](%id = 18446744078126621390), [

          x1a = HFloat(4204.651582462925), 

          x1c = HFloat(4204.651582462925), 

Good morning everybody,

I have to make the Inverse Laplace Transformation of a function which is too complicated and the only way I have is to make it from the points of the function (I can get a plot but maple cannot get the formal form of the function because it is just too big). Does a numerical method exist in maple which can make the Inversion only from the points of the function?

Thank you,

ssteve

How to plot x versus theta of the following implicit function

sin(theta)-2*sin(2*x-theta+(1/3)*Pi)/sin(x+(1/3)*Pi-theta)=0

where x is the implicit function of theta

now how can I plot the relationship between x and theta(condition:-Pi<theta<Pi,-Pi<x<Pi)

How to simplify the following trigonometric expression

sin(w t-theta)+sin(w t-theta-2pi/3)-sin(w t-theta+2pi/3)

to

-2cos(w t-theta+pi/6)

My question is a bit vague, but I hope someone can point me in the correct direction for a solution anyway. A Maple Package was been defined and placed in the Lib folder in Maple 16. The package does contain a number of custom defined functions, say Cos(v) and Sin(v) - with a capital letter to distinguish them from the usual built-in functions in Maple. After having called the package using the with statement, the new function works well in the worksheet. It also works...

Dear Maple Users

I am mainly in favor of the new rules concerning subscripts. Using Ctrl+-- (double underscore) it is pretty straight forward to get a literal subscript and it displays much better in the palette Variables than was the case i Maple 16. Also the purple coloring of a variable containing a literal subscript makes sense, because it can be distinguished from the usual subscript (now Ctrl+shift+-). Good that you can remove the coloring in the View Menu (Atomic Variables...

Hi,

I am trying to find a better way calculating the result of an integral ===>

restart; with(linalg); with(LinearAlgebra);

 E := int(1/(1+A*cos(2*Pi*x))^3, x = 0 .. 1);

u := 1; 

F := Vector(10); 

for A from 0.1e-2 by .1 to 1 do 

F[u] := E; 

u := u+1

 end do;

now I am doing only for 10 points but normally...

Consider the following 2 sets of vectors in R^4: A = {v1, v2, v3}, B = {w1, w2, v3}. You are given that A is a set of linearly independent vectors and that B is a set of linearly independent vectors.

a) The intersection of 2 sets is the set of elements that are common to both sets. Suppose u is in the intersection of span A and span B. Determine a system of equations that could be used to determine all such

Please give specific instructions line per line, and all commands necessary to solve and plot on the same graph the inequality (x+3)^2>(-2)*(x+10).Thank you in advance for your help