Period of a pendulum

The period of a pendulum is the time it takes to perform this oscillation, ie, going back and forth.

In theory, this time depends directly on the length of thread and inversely on the acceleration of gravity, by the equation:

\large T = 2 \pi\sqrt{\frac{\cal l}{g}}

where T is the period, l the length of wire and g the acceleration of gravity, equal to .\large 9,8\frac{m}{s^2}

In this experiment we use an infrared barrier to detect the passage of the thread through a point in his career. You can use any infrared barrier market but on teaching issues, we describe the assembly of that use.

 

Assembly is simple and consists of an infrared LED and an infrared phototransistor, with their respective strengths and . It placed facing the LED and the transistor, so that the light emitted by the first delivered directly to the second. The collector of the transistor is connected to the junction 12 of Arduino, for use in digital form. When the light beam is interrupted, the phototransistor cuts off flow through the collector and Arduino interprets it as a pulse on LOW . If not, it is a high pulse HIGH . The following image is an example of mounting the infrared barrier.220 \Omega10 K\Omega

The assembly of the experience is based on locating the infrared barrier so that the wire crosses the beam twice during its journey. At each junction computes the time elapsed since the previous crossing. The oscillation period is the sum of two consecutive crossings time (trip time plus the back). This value is sent to the serial port for display on the console. Time is taken in microseconds, so you must be divided by 10 6 to convert to seconds, with a resolution of 6 decimal.

The logic is explained in the sketch. The experiment was completed by comparing the periods for various lengths of thread, and for various masses in the end of the thread, in this case checking that the period unchanged. By increasing the mass verify not affect significantly the length of the yarn, stretching it by the weight force.

In the following video of the tests is observed. You can see the pink dot on the LED diode, indicating that it is lighting and LED Arduino transmission that sends the data period every two beam interruptions.

The yarn in this case is 27.5 cm, which in theory gives a period of:

\ Widescreen T = 2 \ most \ sqrt {\ frac {0.275} {9,8 m \ frac {m} {s ^ 2}}} = 1.052526 s

A portion of the list on the console is captured:

1055020
1055728
1054776
1056572
1054936
1055232
1055056
1055508
1055040
1054880
1055232
1054936
1054412

Fairly accurate.

Sketch de Arduino:

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