The Grandfather Clock: The Pendulum By Pat Ryan and Kindra Fuller
Amplitude • The angular displacement from its vertical or equilibrium position. It is measured in terms of the angle that it makes with the vertical.
Frequency • The number of cycles of a periodic process that occur per unit time (second). The unit of measure is the hertz (Hz).
Cycle • Cycle-one full motion from one amplitude position to the other and back again.
Period • Period-the time for one complete cycle of a periodic process and units are in seconds, minutes, etc.
Frequency Equation The equation to calculate the frequency of a pendulum is: f = (1/2pi) * sqrt(g/L) or f = (1/2π) * √(g/L)
Length of Pendulum If you wanted to find the length for a given frequency, you can write that equation as: L = g/(4*pi2*f2) or L = g/(4*π2*f2)
Determining the Period • When given the length of a pendulum, you can find its period by: T=2π√L/g T is the period and g is the acceleration due to gravity. (9.8 m/s2)
Gravity • Value of “g” is Not Constant • Denver Colorado (Mile High City) • On the Moon
1. What happens when you double the mass of the pendulum bob? • The pendulum swings twice as fast • The pendulum swings half as fast • The speed stays the same • 2. What happens if you decrease the length of the pendulum rod? • You decrease the amplitude of the swing • You increase the frequency or rate of the pendulum • You decrease the weight of the bob • 3. How does a pendulum on the Moon compare with one on Earth? • It doesn't work, because there is no air on the Moon • Its frequency would be slower because gravity (g) on the Moon is less than on Earth • Its frequency would be faster because gravity (g) on the Moon is more than on Earth
Sources • www.school-for-champions.com/science/pendulum.htm • www.howstuffworks.com/clock.htm • http//hyperphysics.phy-astr.gsu.edu/HBASE/pend.htmlwww.cpo.com/sc_pendulum.shtml