# Pendulum

We shall take as working example the experiment of the free oscillations in a pendulum.

#### Basic data

The basic data for this experiment, in adequate units, are:
• length = 1800
• m = 1
• g = -800 units

#### Measurement of the free Period

For measuring the Period (1/frequency) of this system we started from a small amplitude situation, set the velocity of the mass to zero, and switch on the clock. Then we measured the elapsed time for three full oscillations (checking the inversion in sign of the x-component of the velocity of the particle):
• HINT for accurate measure of the period: Suppose you want to measure the period in terms of the time needed for 3 full oscillations. The mass starts with zero velocity. Push animate and when the 3rd. oscillation is close to being completed, stop the animation, push "monitor" in the Particle Inspector Panel and continue the oscillation pushing "step" as many times as needed. When the x-component of the velocity has just changed its sign (from + to -), take note of the time elapsed.
The result we measured was:
• T= 28.421875/3 = 9.47396

#### Checking the results:

Theoretical period for small amplitude oscillations is:
• T = 2*p*sqrt(length/g) = 9.4248
(approximately 2*1.5*p).