Methods / ti-cas.org
	The pendulum

1) Compute the period and the frequency of oscillation for a simple pendulum having a length of cord of 43 centimeters.

Activate ME*Pro via APPS.

Choose F3... EQUATIONS, then 8 (oscillations)

Choose 2 (pendulums) then 1 (simple pendulum)

Various equations appear, and F4 (PICTURE) enables you to have a description :

NOTE: the software uses notation GRAV for "g" which is much more familiar for us! ME*Pro uses grav = 9.80665

Select the first and the last equation with ENTER. This will enable us to calculate the period and the frequency of the oscillations.

Press F2 (Solve). The following screen appears:

The length of the cord is 43 centimeters: one enters 43 for L (Note that the toolbar of the preceding screen enables us to choose the measuring unit) (For your information, F5 OPTIONS would have made it possible to make conversions of measurements.)

One supports once again on F2 (Solve) to obtain freq and Tp, and one obtains the opposite screen : Frequency = 0.76 Hz, Period = 1.31 seconds)

2) If a mass weighing 3 kg is attached at the end of the pendulum, what is the maximum tension exerted by the field and the angle of the gravity of displacement for this tension ?

This problem can be solved by two different ways:

METHOD 1: GRAPHIC METHOD

It is necessary to record the weight of the pendulum. We return to the screen of the equations, and we select the second relation. It is then enough to place " 3 kg " in " m ".

ress F3 to pass in Mode GRAPH. The screen enables us to parameterize the plane, and to choose the dependent and independent variables of the equation which we select.

By default, the equation is Tp. We will select Ten.

NOTE: We placed the TI-89 in DEGREES mode via the usual key MODE.

F4 enables us to make a split-screen (SPLIT). When one goes in Graph mode (right), one finds the graphic environment of our TI-89. We used the option F5 MATH ... MINIMUM in order to obtain the minimum of the curve in this window. Here: -29.42. In absolute value, the maximum tension is 29.42 Newtons.

METHOD 2: METHOD BY NUMERIC SOLVER

To calculate Ten (Tension), we select the 3 equations (1, 2, and 4)...

.. and we inform the opposite screen. * téta=0 because the MAXIMUM tension " Ten " is obtained when the pendulum is vertical. * m=3kg It is not necessary to inform " freq " and " Tp " (moreover, it is not very complicated to calculate one period starting from a frequency!) because these values are already known by ME*Pro (first part of the exercise)

Press F2 (Solve)... and... Ten = -29.42. In absolute value, the maximum tension is of 29.42 Newtons.

When you leave the application, you will see that VAR-LINK contains the variables generated by the software. You can thus use them.

This article is only one example of the many possibilities of ME*Pro

It is a powerful tool for the physicists.

It's a shame that ME*Pro is not accessible for all the students (approximately 49 dollars...)

O-Miclo, September 2000