Pendulum Periods
Artur Nisonov (Regents Physics)
Mechanical Engineer
August 30, 2004
Alon Kadashev (Regents Physics)
Electrical Engineer
Overview
Objective
Background
Materials
Procedure
Results
Background
The velocity will be equal to the circumference of the circle which is the
distance traveled divided by the time it took,
v=2πA/ T => T= 2πA/ v
From conservation of Energy => 1/2m(v^2) + 1/2k(x^2)=1/2k(A^2)
Getting the relation=> (A/v)=(m/k)^1/2
Combining all the formulas => T= 2π(m/k)^1/2
Background (cont.)
For small angles => F=-mgsin(θ)~ -mgθ
Arc length => L=xθ
Combining the two equations => F~ -mg(x/L)
According to Hooks law => F=-kx where k=mg/L
Going back to the previous equation T= 2π(m/k)^1/2 substitute for k
and we get T= 2π(L/g)^1/2
Objective
Measure the period of a pendulum as a
function of amplitude
Measure the period of a pendulum as a
function of length
Measure the period of a pendulum as a
function of bob mass
Materials
 Power Macintosh or
Windows PC
 LabPro or Universal
Lab Interface
 Logger Pro
 Vernier Photogate
 Protractor
 String
 Two ring stands and
pendulum clamp
 Mass Bob
 Meter stick
 Graphical Analysis or
graph paper
Procedure





Take a 1 m long string tie it up to the stand on the table.
Attach a Photogate underneath the string, so that when
you attach the mass weight it will pass freely through the
Photogate.
Part I, amplitude test, change the angle three times, and
see how it affects the period.
Part II, length, change the length three times, and
monitor how it affects the period.
Part III, attach three different mass weights and observe
the period will it change, record the data each time.
Results
 Discover that the period is only relation to
the length of the string.
 Find out that T^2 is proportional to L.