15
012-07558A
PAScar Accessory Track Set (2.2 Meter)
®
Experiment 4: Simple Harmonic Oscillator
EQUIPMENT NEEDED:
– PAScar with Mass (ME-6950)
– Dynamics Track
– (2) Springs* (646-04445)
– Super Pulley with Clamp (ME-9448A)*
– Mass hanger and mass set (ME-9348)*
– Stopwatch (SE-8702B)*
– String*
– Mass balance (SE-8723)*
– Graph paper*
Purpose
The purpose is to measure the period of oscillation of a spring and mass system 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 motion,
m
is the mass that is oscillating,
and
k
is the spring constant.
According to Hooke’s Law, the force exerted by the spring is proportional to the distance the
spring is compressed or stretched,
F = kx
, where
k
is the proportionality constant. Thus, the
spring constant can be experimentally determined by applying different forces to stretch the
spring different distances. When you plot the force versus the distance, the slope of the
resulting straight line is equal to
k
.
Procedure
1. Use the balance to find the mass of the car. Record this value at the top of Table 4.1.
2. Level the track by setting the car on the track to see which way it rolls. Adjust the leveling
feet at the ends of the track to raise or lower the ends until the car placed at rest on the track
will not move. Put the pulley with the table clamp at one end of the track.
3. Set the car on the track, and attach a spring to each end of the car by inserting the end of the
spring in the hole provided in the car. Then attach the other ends of the springs to the
endstops (See Figure 4.1).
4. Attach a string to the end of the car, and hang a mass hanger over the pulley as shown.
5. Record the equilibrium position in Table 4.1.
6. Add mass to the mass hanger and record the new position. Repeat this for a total of 5 differ-
ent masses, being careful not to overstretch the springs. Because both springs are acting on
the mass, this method will give the effective spring constant for both springs.
*Not included in Track Set
T
= 2
π
m
k
Measurements to Find the Theoretical Period
Summary of Contents for ME-6956
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