Experiment 4a: The Slinky and the Ideal Spring Static Deflection

This experiment is performed to observe the behavior of a slinky when mass is added and determine its spring constant. The results will be compared to the Ideal spring and the springs that where experimented in previous laboratory. Other springs have a circular cross section thus having a tension and compression side while the slinky has a thin rectangular cross section allowing one to assume it has a stress-free neutral axis.

Table 1 shows results for slinkyMass(kg)T(m)

00

0.0050.07

0.0010.012

0.00150.018

0.0020.021

This Plot shows results for Spring Constant

Figure 1The Spring Constant for the slinky is the slope of the trend line or 1.0805 N/mTable II: Spring Constant comparison

Spring Constant

SlinkyRedWhite

1.0805

Table III: Intercept (grams)

Intercept (grams)

ExpectedSlinkyRedWhite

01

The comparison of the springs and the slinky shows that the slinky is closer to being an Ideal spring compared to the other springs and has a more linear graph of force vs. elongation.

Experiment 4b: The Slinky as an Ideal Spring: Vibrating Frequency, Spring ConstantApproach

This experiment aims to determine and compare the vibrating frequency of an ideal spring and the slinky using the spring constant without a mass attached to it. Only the weight of the spring causes it to vibrate. Determining the Experimental value for frequency:

Determining the Calculated value for frequency:

Determining effective mass using Eq.3

Determining effective mass using Eq. 5

Table I: ResultsResults

t(s)T(s)(sec/cycle)(rad/s)Effective Mass, me

ExperimentalCalculatedEq.3Eq.5

12sec1.2s0.0177kg0.0394kg

The results for the effective mass has a relatively large % of error, this may be caused by the inaccuracy of the period.