 |
| You Try It! |
| (1) Copy a word problem from a book (or make up one of your own) and solve the problem using Maple. The format should look like Print Format below. Be sure to join the execution groups in a similar fashion. |
| The Differential Equations Take Home Quiz |
| by Bob Bradshaw |
| Plot the differential equation on a plot with t on the x-axis and position and velocity on the y-axis. Then make a phase plane of the answer. |
|
 |
 |
| with(plots): with(DEtools): eqn1:=diff(x(t),t) = y(t); eqn2:=diff(y(t),t) = -1/1*x(t)-0/1*y(t); ic:=[[x(0)=0,y(0)=4]]; vars:=[x(t),y(t)]: p:=dsolve({eqn1,eqn2,x(0)=0,y(0)=4},vars,type=numeric): y1plot:=odeplot(p,[[t,x(t)]],0..10,numpoints=100,color=red,labels=["Time","Position"],title="Position as a Function of Time"): display(y1plot); y2plot:=odeplot(p,[[t,y(t)]],0..10,numpoints=100,color=blue,labels=["Time","Velocity"],title="Velocity as a Function of Time"): display(y2plot); |
 |
 |
 |
 |
 |
| Here is the phase plane diagram of the systems of differential equations: |
| eqn1:=diff(x(t),t) = y(t); eqn2:=diff(y(t),t) = -1/1*x(t)-0/1*y(t); ic:=[[x(0)=0,y(0)=4]]; vars:=[x(t),y(t)]: DEplot({eqn1,eqn2},vars,t=0..24,ic,linecolor=[black],title="Undampened Pendulun Phase Plane",stepsize=0.01,scaling=constrained); |
 |
 |
 |
 |
| (2) Convert the solution of your problem into an outline using sections. See Screen Format. |
| Title and Author |
| The Differential Equations Take Home Quiz |
| by Bob Bradshaw |
| Statement of Problem |
| A:Plot the differential equation on a plot with t on the x-axis and position and velocity on the y-axis. Then make a phase plane of the answer. B: Make the phase plane diagram of the systems of differential equations. |
 |
 |
 |
| Part A |
| with(plots): with(DEtools): eqn1:=diff(x(t),t) = y(t); eqn2:=diff(y(t),t) = -1/1*x(t)-0/1*y(t); ic:=[[x(0)=0,y(0)=4]]; vars:=[x(t),y(t)]: p:=dsolve({eqn1,eqn2,x(0)=0,y(0)=4},vars,type=numeric): y1plot:=odeplot(p,[[t,x(t)]],0..10,numpoints=100,color=red,labels=["Time","Position"],title="Position as a Function of Time"): display(y1plot); y2plot:=odeplot(p,[[t,y(t)]],0..10,numpoints=100,color=blue,labels=["Time","Velocity"],title="Velocity as a Function of Time"): display(y2plot); |
 |
 |
 |
 |
 |
| Part B |
| eqn1:=diff(x(t),t) = y(t); eqn2:=diff(y(t),t) = -1/1*x(t)-0/1*y(t); ic:=[[x(0)=0,y(0)=4]]; vars:=[x(t),y(t)]: DEplot({eqn1,eqn2},vars,t=0..24,ic,linecolor=[black],title="Undampened Pendulun Phase Plane",stepsize=0.01,scaling=constrained); |
 |
 |
 |
 |
| (3) Create a web page showing your solution. |
| You will most likely want to see the original maple input for this one. |
| Formatting |
 |