PASCO ME-6962 PAStrack Systems - Manual (Page 18)

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P A S t r a c k S y s t e m s E x p e r i m e n t 5 : S p r i n g s i n S e r i e s a n d P a r a l l e l
18
Experiment 5: Springs in Series and Parallel
Purpose
In this experiment, you will measure and compare the periods of oscillation of a cart
attached to various combinations of springs.
Theory
For a mass attached to a spring, the theoretical period of oscillation is given by
where T is the time for one complete back-and-forth cycle, m is the mass that is oscil-
lating, and k is the spring constant. If the period of oscillation is measured, the spring
constant can be determined by
You will determine spring constant of a spring by measuring the period of oscillation
and mass of a cart attached to the spring. You will use the same method to determine
the effective spring constant of two identical springs combined in series and in paral-
lel. For each type of combination, you will discover the relationship between the
spring constant of the single spring and the effective spring constant of the combina-
tion.
Procedure
Measuring the Spring Constant of a Single Spring
1. Measure the mass of the cart. Record this value at the top of Table 5.1.
2. Install the end stop on the track near one end.
3. Set the cart on the track and attach a spring to one end. Attach the other end of the
spring to the end stop (see Figure 5.1).
Required Equipment from PAStrack System
PAStrack
(2) End Stops
PAScar
Pivot Clamp
Harmonic Springs (2)
Other Required Equipment Suggested Model Number
Base and support rod ME-9355
Stopwatch ME-1234
Mass balance SE-8723
T 2  m
k
---- =
k
4 
2
m
T
2
------------- =