Pendulum Modeled by Motion on a Circle

For this exercise you will use the program SHMRLTM1 from CD #1 (just browse to the disk1.htm file in the root folder and run that file, which will give you a menu).  Download or just run the program from that location.

The program is easily run by just hitting keys on the keyboard. 

Smaller/larger:  SsLl

s makes the circle a little smaller, S makes it smaller more quickly

l (lower-case L)  makes the cirlce a little larger, L causes a bigger jump in size

Floor it  FfRr

r increases the angular frequcycy by .001 radian / second

R, f and F increase angular frequency by .01, .1 and 1 radian / second, respectively

Brakes:  BbGg

B, b, G and g decrease angular frequency by 1, .1, .01 and .001 rad / sec, respectively

Omega: a

if you hit the a key you will be prompted to specify the angular frequency, which you can just type in and Enter

Note that the pause button apparently doesn't work.

Note also that to Quit the program you can just hit the q key.

The simulation shows a circle, with a point moving around the circle, and the vertical and horizontal lines through the point.  The vertical line traces the x coordinate of the point, and the horizontal line traces the y coordinate.

The Exercise

Tie a thin string or a thread around a weight to make a pendulum.  A bolt or a washer makes a good choice, but you can use just about anything that is pretty small and dense.

• With the simulation running, hold the pendulum in front of your computer screen so that it hangs right in front of the center of the circle, keeping the top fixed (i.e., don't let the top end of the string move around) and let it oscillate in front of the screen.
• Adjust the speed of the simulation and the radius of the circle until the pendulum stays exactly in front of the vertical line which moves left and right across the screen.
• Make note of the angular velocity of the point moving around the circle, which is given at the bottom of the screen.  This angular velocity is measured in radians / second.

Note that the vertical line gives you the x coordinate of the position of the point.  We make the convention that x = 0 at the center of the circle.  So depending on the size of your screen and the radius of the circle, x will vary from a couple of inches in the positive direction to a couple of inches in the negative direction.

The point of this exercise is to understand that the position of the pendulum can be modeled by the horizontal coordinate of the reference-circle point.

Motion which can be modeled by the vertical or horizontal coordinate of a point moving around a reference circle is called Simple Harmonic Motion.  The equations that describe the motion involve the sine and cosine functions, which are the basic trigonometric functions we study in this course.

• Email the instructor with the length of the pendulum, from the fixed point at top to the center of the object you tied to the string, and the angular velocity.