PASCO ME-6956 2.2 m PAScar Dynamics System - Manual (Page 14)

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2 . 2 m P A S c a r D y n a m i c s S y s t e m E x p e r i m e n t 4 : O s c i l l a t i o n s o n a n I n c l i n e
14
Experiment 4: Oscillations on an Incline
Purpose
In this experiment, you will measure the period of oscillation of a spring and mass
system on an incline at different angles and compare it to the theoretical value.
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.
According to Hooke’s Law, the force exerted by the spring is proportional to the dis-
tance, x, by which the spring is compressed or stretched, F = kx, where k is the pro-
portionality constant. The spring constant can be experimentally determined by
applying different forces to stretch the spring different distances. When the force is
plotted versus distance, the slope of the resulting straight line is equal to k.
Procedure
Measurements to Find the Spring Constant and Theoretical Period
1. Measure the mass of the cart and record it in Table
4.1.
2. Instal 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 an the end
stop (see Figure 4.1).
4. Incline the track by raising the end of the track where the spring attached. As the
end of the track is raised the spring will stretch. Keep the angle of inclination of
the track small enough so the spring is not stretched more than about 50 cm. Use
Required Equipment from Dynamics System
Track with End Stop
PAScar
Pivot Clamp
Other Required Equipment Suggested Model Number
Harmonic Spring ME-9803 (3-pack)
Base and support rod ME-9355
Mass hanger and mass set ME-9348
Stopwatch ME-1234
Mass balance SE-8723
T 2
 m
k
---- =
q
Figure 4.1: Equipment Setup