Worksheet #1 - PHY 102 (Spr. 2005)
Due Thursday Jan. 20th at 9:30pm
This worksheet introduces you to the use Mathematica. Mathematica is a programming language developed by Stephen Wolfram which has many applications,e.g., solving algebraic equations, differentiation, integration, making plots in two and three dimensions, etc.. You will also solve a couple of simple problems in mechanics using Mathematica. The reference material for this worksheet is in sections 1.0.1 to 1.1.7 of the practical introduction to mathematica . You should read this material as you work through the exersizes below. A brief introduction to Mathematica is also available on the course www page (written by Ellen Lau).

Getting Started

1. Click on the start'' button in the lower left corner of the screen.

2. Move the cursor Programs Mathematica Mathematica ''

3. Click on Mathematica.

4. Under the format menu click on Show Toolbar''

5. Again, go the format menu and click on Screen Style Condensed''

You will now get a screen where you can carry out the following simple exercises to get an idea of how to use Mathematica.

i) Type 2+4'' and hold down the shift'' button in the key board and push enter'' (each time you want to get the result for what you have typed, you have to type shift+enter''). In the output the screen will give you back the result.

ii) Type 10/2'' to check that you'll get 5 in the output.

iii) To find the roots of an equation (e.g. x2-1), type Solve[x2-1 == 0,x]''. In the output you'll get +1 and -1 as the two roots.

iv) You can do much more! You can factorize the expression x2-1 as we usually do to get the roots. In order to do that type Factor[x2-1]'', and check if you get (x+1)(x-1).

v) Mathematica has extensive plotting tools. For example plot the function sin(x). To do this type Plot[Sin[x],{x,0,6.28}]''.

vi) Help??? Mathematica has an extensive online help library. Try looking up the sin(x) function to make sure you have the right format.

vi) Here is an example how you can perform differentiation using mathematica: suppose f(x) = xn; then . To check it type D[xn, x]'' and see the output.

vii) Likewise, you can perform integration on f(x) = xn. Type Integrate [xn, x]'' and assure yourself that you indeed get back .

Assignment 1. - Hand in by Thursday Jan. 20th
Examples. Hand in the results of 10 mathematica operations you experimented with.

Problem 1. The displacement of a particle undergoing one dimensional motion under constant acceleration is given by the equation . Choose values of u and a that you think are physically reasonable. Find and plot x(t) and v(t) over a reasonable range of time (this depends on your choice of u and a). Note: In plotting, use Plot[Evaluate[x[t]],{t,0,5}]'' after defining x[t].

Problem 2 The velocity of a particle is given by v(t) = 0.10 t - cos(2t) in the positive x direction. At t=0, it was located at x(0)=0. Find and plot x(t) for t up to 10s.