Oscillation of springs

By: Yanfei Zhao

Lab partner: Xinao Chen
TA:
Date: September 25, 2014

Introduction: The purposes of this lab is to observe and analyze the factors behind a static mass on a spring and the simple harmonic motion that is generated by an oscillating mass on a spring. The principle determining factor for the motion of the spring is its spring constant K as defined by Hooks Law. Hooks Law says that the force generated by a spring is proportional to the displacement of the spring from its rest position multiplied by the spring constant. Hooks Law is defined in the equation:

Where: F is the force generated by the spring in Newtons (N). X is the displacement of the spring from its rest position in Meters (m). K is the spring constant for that certain spring in Newtons/Meter (N/m).
The rest position of a spring is the position the spring is in without and stretches or compressions. Spring constants vary and is only specific to a certain spring.
The spring itself has mass and therefore it has its own inertia which will affect its oscillation by adding mass to the system. When analyzing oscillations, the mass of the spring must also be accounted for. The mass of a spring and the period of oscillation can be determined with the equation:

Where: T is the period of oscillation is seconds (s). M is the mass suspended from the spring in kilograms (kg). ms is the mass of a cylindrical spring in kilograms (kg).

Experimental Method: The lab was performed by attaching different combinations of 0.100kg, 0.025kg and 0.050kg mass onto a hanging cylindrical spring. The first set of data was collected while the spring was not in motion and was done with 0.250kg and 0.450kg masses. The second set of data was collected with the spring in simple harmonic motion beginning with a starting mass of 0.250kg of mass hung from the spring. Each successive test would increase the mass by 0.025kg ending at a final mass of 0.450kg. A motion sensor call “Logger pro” was used to measure the distance between the bottom of the mass and the ground.

Pictures of lab apparatus:

Results:
1. Table #1: Position of a 0.250kg mass on a spring as a function of time.
Latest: Time (s)
Latest: Position (m)
0.05
0.799
0.1
0.797
0.15
0.796
0.2
0.796
0.25
0.796
0.3
0.798
0.35
0.798
0.4
0.798
0.45
0.798
0.5
0.798
0.55
0.798
0.6
0.798
0.65
0.799
0.7
0.799
0.75
0.799
0.8
0.799
0.85
0.799
0.9
0.799
0.95
0.799
1
0.797
1.05
0.799
1.1
0.797
1.15
0.796
1.2
0.798
1.25
0.798
1.3
0.798
1.35
0.798
1.4
0.798
1.45
0.798
1.5
0.798
1.55
0.798
1.6
0.798
1.65
0.798
1.7
0.798
1.75
0.798
1.8
0.798
1.85
0.797
1.9
0.796
1.95
0.799
2
0.799
2.05
0.799
2.1
0.799
2.15
0.798
2.2
0.798
2.25
0.798
2.3
0.798
2.35
0.798
2.4
0.798
2.45
0.797
2.5
0.798
2.55
0.797
2.6
0.796
2.65
0.796
2.7
0.798
2.75
0.796
2.8
0.796
2.85
0.798
2.9
0.799
2.95
0.799
3
0.799
3.05
0.799
3.1
0.799
3.15
0.799
3.2
0.799
3.25
0.799
3.3
0.799
3.35
0.799
3.4
0.798
3.45
0.799
3.5
0.798
3.55
0.798
3.6
0.798
3.65
0.798
3.7
0.796
3.75
0.796
3.8
0.798
3.85
0.798
3.9
0.798
3.95
0.799
4
0.799
4.05
0.797
4.1
0.797
4.15
0.799
4.2
0.799
4.25
0.799
4.3
0.799
4.35
0.799
4.4
0.799
4.45
0.799
4.5
0.799
4.55
0.799
4.6
0.796
4.65
0.796
4.7
0.796
4.75
0.796
4.8
0.796
4.85
0.798
4.9
0.799
4.95
0.799
5
0.799
5.05
0.799
5.1
0.799
5.15
0.797
5.2
0.797
5.25
0.797
5.3
0.797
5.35
0.797
5.4
0.797
5.45
0.797
5.5
0.797
5.55
0.797
5.6
0.797
5.65
0.797
5.7
0.797
5.75
0.796
5.8
0.798
5.85
0.799
5.9
0.797
5.95
0.798
6
0.798
6.05
0.797
6.1
0.799
6.15
0.799
6.2
0.799
6.25
0.799
6.3
0.799
6.35
0.8
6.4
0.799
6.45
0.799
6.5
0.799
6.55
0.799
6.6
0.799
6.65
0.797
6.7
0.799
6.75
0.797
6.8
0.796
6.85
0.796
6.9
0.797
6.95
0.796
7
0.796
7.05
0.796
7.1
0.796
7.15
0.797
7.2
0.799
7.25
0.799
7.3
0.799
7.35
0.799
7.4
0.799
7.45
0.799
7.5
0.797
7.55
0.797
7.6
0.799
7.65
0.799
7.7
0.799
7.75
0.799
7.8
0.797
7.85
0.797
7.9
0.796
7.95
0.796
8
0.796
8.05
0.796
8.1
0.796
8.15
0.796
8.2
0.797
8.25
0.797
8.3
0.797