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.

T = 2π

 

 

R

 

 

g

 

 

 

R(cm)

: Pendulum Length

g(cm/s2) : Gravitational Acceleration

m(g)

: Mass of Weight

T(s)

: Period

1Fixed 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/s2 and the length of the pendulum is 25cm, the oscillation period of the pendulum is about one second.

2-2-1

English

Activity:tivity: SetupSetup

￿Equipment

String with little elasticity Weight Stand Height adjustment blocks (2)

Optical Measurement Setup (EA-200, graphic scientific calculator, data communication cable, optical probe)

￿Building a Pendulum

uSecuring the fixed point of the pendulum so it cannot move, assemble the pendulum as shown in the illustration.

1Stand

2Pendulum Length: 30cm

3Fixed Point

4String

5Weight: 100g

6Weight Size: 3cm

7Height: 2cm

8Desk

￿Setting Up

uAlign the heights of the optical probe and flashlight so the flashlight is shining directly at the probe.

uSet up the pendulum so the weight blocks the light to the optical probe when it is at rest.

1Flashlight

2Optical Probe (Observer) (CH1)

3EA-200

4Distance Between Weight and Optical Probe: 10cm

5Desk

20020601