Vibratory Motion Of A Spring

2 Pages 595 Words

Lab: Vibratory Motion of a spring

Purpose: To verify the laws of simple harmonic motion for the spring.

Materials: Spring, mass holder with pointer, scale, slotted masses, timer

Procedure:
1. Determine the force constant of the spring by adding masses to the spring, one at a time. There should be at least six mass increments. Unload the spring, one mass at a time, and note the elongation. Plot a graph of force vs. elongation and take the slope of the line.
2. Determine the time for one complete vertical oscillation (period). To do this, attach the first known mass and pull the spring slightly from down its equilibrium position and release it. The system is now oscillating. Record the time for 50 complete oscillations and then determine the period. Repeat with the same mass increments you used in procedure 1.
3. Theory suggests the period, T, is related to the spring constant, k, by equation (5). Plot a graph of T vs. mass effective. Determine the value of k from the graph and compare it to the value of k that you determined in procedure 1.

Hypothesis: I believe that the k value from the first graph (force vs. elongation) will be very close if not equal to the k value of the second graph (period^2 vs. effective mass).

Data:
Increment Mass (m) Applied Force Elongation x loading Elongation x unloading
No. kg N m m
1 0.325 3.185 0.232 0.19
2 0.425 4.165 0.269 0.19
3 0.525 5.145 0.31 0.19
4 0.625 6.125 0.349 0.19
5 0.725 7.105 0.384 0.19
6 1.025 10.045 0.498 0.19
Mass of spring = .075 kg

Trial Effective mass (m) Time for 50 vibrations Period (T) Period (T^2)
No. kg s s s^2
1 0.325 36.28 0.7256 0.526495
2 0.425 40.62 0.8124 0.659994
3 0.525 44.93 0.8988 0.807841
4 0.625 48.43 0.9686 0.938186
5 0.725 52.32 1.0464 1.094953
6 1.025 61.63 1.2326 1.519303


Questions:
1. The plot of the force versus elongation indicate that the spring obeys Hooke’s Law because the formula F = -...