Physices data repoert (only abstract and result)

Mashan Alshammari

Annabel Garcia

Mackinzee Griebel

4/6/2017

Lab 9: Simple Harmonic Oscillator

Abstract: The purpose of this lab was to verify that the period of the spring-mass system is dependent on mass, spring constant, and amplitude when the system is acting as a simple harmonic oscillator. During this lab, the material and equipment that were used was a computer with PASCO 850 Universal Interface and PASCO Capstone, a vertical stand with an additional horizontal cross bar, the PASCO Motion Sensor, a spring kit, a mass hanger, and a set of masses. The experiment was composed of four parts: the first part was measuring the spring-mass system for period, the second part was measuring the period while changing the spring constant, the third part was measuring the period while changing the mass, and the final part was measuring the period while varying the amplitude. The PASCO Capstone file titled “Simple Harmonic Oscillator” helped tremendously in getting the experiment data for the experiment parts 1-4. The PASCO Motions Sensor was connected to the PASCO interface, and for each part of the lab the sensor was correctly oriented at 90° below each spring. During part 1, a green spring with a spring constant (k) of 50 N/m was used. Then a 0.500 kg mass was added to the spring, and the mass was pushed down and released in order to create an oscillation. From the PASCO Capstone file, the time from peak to peak from the oscillation was obtained, and by using the equations, the frequency (f) and the period (T) were determined. Next in part 2, there were more springs involved, which were red with 25 N/m, blue with 30 N/m, yellow with 35 N/m, and white with 40 N/m. The same mass of 0.500 kg was used for each spring, and the springs were pushed down in order to create an oscillation, which was recorded. The reason different springs with different spring constants were used was to determine the relationship between the spring constant and its period and frequency when using the same mass. Graph one is verifying that the frequency is indeed proportional to the square root of the spring constant, without doing so the graph would not express a linear relationship that is often described by the formula 𝑓 = (1/2𝜋) √ 𝑘/𝑚 or 𝑓^2 = (1/4𝜋^2)𝑚/𝑘. In part 3, the green spring was used, and the mass was increased from 0.300kg, 0.400 kg, 0.500 kg, 0.700 kg, and 0.750 kg for the five trials, respectively. The same procedure was used to create the oscillations, and the trials were recorded. This part of the lab was to determine the relationship that the mass had on the oscillation’s period and its frequency. Graph two is verifying that the period is proportional to the square root of the mass, had the period not been squared the linear relationship would not have followed this specific trend. The trend is often described by the formula 𝑇 = 2𝜋√𝑚/𝑘 T^2 = 4𝜋^2 𝑘/𝑚. In part 4, the purpose of this part was to determine the relationship between the oscillation’s period and frequency with the amplitudes changing. The green spring, which has a spring constant of 50 N/m, and a mass of 0.400 kg were used. The amplitudes were recorded at increasing rates for each trial.

The result:

Peak number (GREEN)	1	2	3	4	5
time (s)	0.18	0.86	1.54	2.2	2.88
period (s)	0.68	0.68	0.66	0.68
average period (s)	0.68
frequency (Hz)	1.48

Table 1. Measured and Calculated values for an oscillator using a 50 N/m spring.

Color of the spring	Green	White	Yellow	Blue	Red
Spring Constant (N/m)	50	40	35	30	25
Frequency	1.48	1.32	1.22	1.13	1.05
Squared Frequency (Hz2)	2.19	1.73	1.49	1.28	1.10

Table 2. Oscillation frequencies of all of the springs while using a 0.5 kg weight.

Graph 1: Frequency squared of all of the springs vs their corresponding constants.

Suspended mass (kg)	0.5	0.7	0.75	0.3	0.4
Frequency (Hz)	1.48	1.67	1.23	1.87	1.64
Period (s)	0.68	0.85	0.81	0.54	0.61
Squared Period (s2)	0.46	0.72	0.66	0.29	0.37

Table 3. Oscillation frequencies for varying masses that are hanging from the 50 N/m spring.

Graph 2: Period squared of the spring using different corresponding masses.

Amplitude (m)	0.24	0.26	0.27	0.3	0.34
Period (s)	0.61	0.61	0.62	0.62	0.61

Table 4. Oscillation frequencies for the 50 N/m spring with the same 0.4 kg mass only varying with light touch to rough touch.