PASCO ME-9429B 1.2 m Classic Dynamics System - Manual (Page 15)

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M o d e l N o . M E - 9 4 2 9 A E x p e r i m e n t 3 : S i m p l e H a r m o n i c O s c i l l a t o r
15
Experiment 3: Simple Harmonic Oscillator
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, F, exerted by the spring is proportional to the
distance, x, by which the spring is compressed or stretched: F = kx, where k is the
spring constant. Thus the spring constant can be experimentally determined by apply-
ing different forces to stretch the spring different distances. If 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 3.1.
2. Instal the feet on the track and level it.
3. Instal the end stops about 1 m apart.
4. Clamp the pulley at one end of the track.
5. Set the cart on the track and attach a spring to each end. Attach the other ends of
the springs to the end stops (see Figure 3.1).
Required Equipment from Dynamics System
Track with Feet and End Stops
Cart
Super Pulley with Clamp
Harmonic Springs (2)
500 g Cart Mass
Other Required Equipment Suggested Model Number
Mass hanger and mass set ME-9348
Stopwatch ME-1234
Mass balance SE-8723
String (about 2 m)
Graph paper
T 2
 m
k
---- =