Period Of Pendular Movement - Casio EA-200 User Manual

Period of Pendular Movement

In this activity, we create a simple pendulum and then visually check the periodicity of its
movement, while determining its period.
Theory
A pendulum is a string whose one end is fixed and whose other end has a weight attached
to it. As the weight swings, it keeps returning to the same position at the same velocity over
time. Such motion is called "periodic motion," and the time it takes for the weight to return to
a particular state is called its "period." A high-precision pendulum can continue to swing for
a very long time with little change in its period over time. This is why such a pendulum is
often used for timepieces.
A pendulum that moves across a single plane is called a simple pendulum. When the
amplitude of the pendulum is sufficiently short in relation to its length, the period of a simple
pendulum can be expressed as shown below.
R
T = 2π
g
R
(cm) : Pendulum Length
g 2
(cm/s ) : Gravitational Acceleration
m
(g) : Mass of Weight
T
(s) : Period
1 Fixed Point
All of this means that if gravitational acceleration is a fixed value that depends on the
location where the activity is performed, then the period depends on the length of pendulum
only.
With this activity, a pendulum is setup between a light source and an observer. The shadow
created by the weight makes it possible to observe the periodicity of the pendular motion.
Though actual gravitational acceleration depends on latitude and elevation, this activity can be
conducted using the gravitational constant. When gravitational acceleration is 980cm/s
the length of the pendulum is 25cm, the oscillation period of the pendulum is about one second.
2-2-1
English
í Equipment
String with little elasticity
Optical Measurement Setup (EA-200, graphic scientific calculator, data communication
cable, optical probe)
í Building a Pendulum
u Securing the fixed point of the pendulum so it cannot move, assemble the pendulum as
shown in the illustration.
1 Stand
2 Pendulum Length: 30cm
3 Fixed Point
String
4
Weight: 100g
5
6 Weight Size: 3cm
7 Height: 2cm
8 Desk
í Setting Up
u Align the heights of the optical probe and flashlight so the flashlight is shining directly at
the probe.
u Set up the pendulum so the weight blocks the light to the optical probe when it is at rest.
Flashlight
1
2 Optical Probe (Observer) (CH1)
3 EA-200
Distance Between Weight and Optical Probe: 10cm
2 and 4
5 Desk
20020601
Activity: Setup Activity: Setup
Weight Stand Height adjustment blocks (2)