Lab 10 Report

Simple Harmonic Motion

Abstract: The experiment was done in order to determine whether or not simple harmonic motion follows Hooke’s law. The experiment consisted of two parts, the first part was done with springs hanging weights as well as the pulling down of a string attached to the spring for both individual and two springs. The second part was done with a collision cart and springs attached on both ends of the cart. The data obtained supported that simple harmonic motion obeys Hooke’s law as the spring value constants were all positive and the graphs displayed a positive slope. The percent discrepancy obtained for one spring was 14.66% and the percent discrepancy for two springs was 0.375%.

Objective:
The physics concept being studied from this experiment is the spring constant and simple harmonic motion.

Equipment
Part 1
Two nearly identical springs
Long rubber band
Support stand with a meter stick
50 g mass hanger
Set of masses from 100 g up to 600 g
Balance scale
Science workshop interface with force sensor and rotational motion detector used as linear sensor
Part 2
Collision cart of known mass on horizontal dynamics tracks oscillating by the means of a springs in parallel
Motion sensor and photogate connected to Science workshop interface
Non-linear springy objects (rubber bands)
Two rectangular weights of ~0.5 kg each to change the mass of the system

Procedure:
The lab experiment was done in two parts. Part 1 of the experiment was done by 2 different methods. Method 1 was with a force sensor, springs, and a weight hanger in which masses of 100 gram increments were added (up to 600 grams). A force vs. displacement graph was created and the slope of the graph was recorded. By method 2 the force sensor was tare with a 1 kilogram weight. After the force sensor had been tare a spring was added in place of the 1 kilogram weight then a piece of string was attached at the end of the spring. The string was then pulled counterclockwise through the rotation motion sensor until the sensor read 10 Newton’s. An elastic force vs. displacement graph was created and the slope was recorded (displays force constant), as well a force vs. position graph. Method 2 was then repeated with a nonlinear object (rubber band) instead of the string, a graph was made comparing force vs. position and the slope was recorded to determine whether or not a rubber band follows Hooke’s law.

Part 2 of the experiment was done with a collision cart on the horizontal dynamics track. Two springs were hooked onto each end of the collision cart. The cart is then pulled 4 cm towards one end of the track and released. The period was recorded and the procedure was repeated with lengths of 8 cm and 12 cm. Once all three trials had been done a position vs. time and a velocity vs. time graph was created.

Data Analysis
Part 1: 1 Spring

Part 2: 2 Springs

Part 3: Oscillating Cart

Results
Part A

Experimental spring constant k (N/m)
Theoretical spring constant k (N/m)
Percent Discrepancy
Percent Error
Spring 1
36.69 N/m
32.00 N/m
14.66%
4.830%
Spring 2
31.88 N/m
32.00 N/m
0.3750%
0.3010%

Part B

Experimental spring constant k (N/m)
Spring in Series
16.6 N/m
Spring in Parallel
64.6 N/m

Part C

Experimental spring constant k (N/m)
Oscillating Cart
0.7489 N/m Discussion
The physics concept being studied here is Hooke’s law as it relates to simple harmonic motion. Based on the graphs produced by spring 1 and spring 2, the springs obey Hooke’s law as the force needed to stretch the springs is proportional to the distance that they are stretched. This can be seen as the graphs are both positively linear. The spring constant of two springs is about half of the spring constant of an individual spring. The rubber band also follows Hooke’s law as it is a positive linear slope. Based on the collected data the larger the amplitude the shorter the period and vice versa. The law of conservation of energy was not upheld in my experiment however the values are fairly close. The main characteristics of simple harmonic motion is net force is proportional to displacement from equilibrium point and is directed toward the equilibrium point.

Conclusion
The objective of the lab “Simple Harmonic Motion” was met. From the lab I learned that springs obey Hooke’s law which is F=kx and the distance that the spring is stretched is proportional to the force required.