7. Simple Harmonic Motion

pdf

School

Stony Brook University *

*We aren’t endorsed by this school

Course

133

Subject

Electrical Engineering

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by KidSwanPerson1009

Sakhi Thakkar November 5, 2023 PHY 133 TA: Fabiola Caeteleyva Simple Harmonic Motion

Introduction In this lab, I will finding the angular frequencies which are found experimentally and theoretically of a simplicity harmonic oscillator. Along with this, the peak frequency will also be found using the Fast Fourier Transform. In the end, I will test the relationship of mass and the angular frequency to see if the expected results of adding more mass results in the decrease of angular frequencies. Simple Harmonic motion is the type of oscillation motion, where the restoring force force is directly proportionate to the displacement. The restoring force works in the opposite orientation of the displacement. Methods/Procedure Equations used: 1. Newtons Second Law 2. Displacement, velocity, and acceleration -x(t)=Acos ω t -v(t)=-A ω sin ω t -a(t)=-A ω ^2cos ω t 3. Frequency and period -T=1/f -f=1/f 4. Relation between angular frequency and period -T=2 π / ω Procedure I: finding the known mass 1. Replace the plate, then fasten the screw 2. Position the device on its head with the y direction pointing down 3. Press record. Let the device sit on the table for one second then steadily lift the device by the screw 4. Place it back down and stop recording 5. After, find the average force and acceleration. This will give you the force and the acceleration due to gravity 6. Use gravitational force equation to find the mass Procedure II: finding the period and frequency 1. Attach a long spring to the device, hang the device using a paper clip, and allow it to oscillate for a minute 2. Calculate the the time of the first five peaks and divide it by 4 to find the period 3. Using the period, find the angular frequency 4. Then calculate the the peak frequency by using the FFT, then calculate the angular frequency, and compare the two frequencies 5. Repeat two more times to get the angular frequencies for the two added masses

Results Procedure I: finding the known mass 1. Data to find average force 2. Data to find average acceleration Mass number 1

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Procedure II: finding the period and frequency TRIAL 1 (mass number 1) The angular frequency using the period, it came out to 6.4. Comparing it to the angular frequency using the Fast Fourier Transform, it came out to 7.9. The difference between these values is 1.5. - Time between the first 5 peaks : 3 . 95s - Period : 3 93/4 =0 985 - Angular frequency (using period) : T = 2 π /w 0 . 98 = 21/0 W = 25/0 98 6 . 4 radian /S - Peak frequency : 1 . 270Hz - Angular frequency (using peak frequency) : W = 2 if W = 2 1 270 W = 7 . 9 radian/s

Mass number two 1. Data to find average force 2. Data to find average acceleration

Procedure II: finding the period and frequency TRIAL 2 (mass number 2) The angular frequency using the period, it came out to 5.3. Comparing it to the angular frequency using the Fast Fourier Transform, it came out to 6.7. The difference between these values is 1.4.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Mass N umber 3 1. Data to find average force 2. Data to find average acceleration

Procedure II: finding the period and frequency TRIAL 3 (mass number 3) The angular frequency using the period, it came out to 4.4. Comparing it to the angular frequency using the Fast Fourier Transform, it came out to 5.5. The difference between these values is 1.1.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Calculations

Discussion/Conclusion In this lab, the mass of the IOLab device was found and two other masses by adding on objects to the IOLab device was also found along with their angular frequencies. The period from the beginning of the run compared to the period from the end of that same run becomes larger. All the angular frequencies that where calculated were very close and the more trials performed and more the mass was increased, they became closer. Starting with the angular frequencies difference calculated form the period and peak frequency from run one, it was 1.5, then in run two it was 1.4, then in the final run it was 1.1. The square root of 11.5 is 3.3 and the A value from the angular frequency vs mass of the object graph is 2.806. There is a slight difference in these values, but they are quite close so it does make sense. To conclude the lab, through many trials no observed outliers where in the data. Some sources if error could of been human error such as not properly taping the object to the IOLab device. In the end, this lab was a success and the hypothesis was proven true that the expected results was when more mass is added, the angular frequencies decrease.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version