Old Dominion University
PHYS 111N
Experiment 10 Harmonic Motion
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Lab Partner:
Lab Instructor:

Introduction
In this experiment we will investigate the simple harmonic motion of an object suspended by a spring that oscillates on a vertical plane and in a separate experiment was examine oscillations on a horizontal plane. In simple harmonic motion, the displacement from the equilibrium position is directly proportional to the force. The force generated is always directed toward the equilibrium position. If the object is at its vertical peak and descending, the force is directed downward toward the point of equilibrium. The same is true for the objects in a vertical system or a horizontal system. Because the force always is directed towards the equilibrium position it is referred to as the restoring force.

The spring constant of the springs used in the experiment must be calculated prior to performing any additional step. This is done using the Pasco Scientific Data Studio and equipment. We set up the 36” vertical support rod on the table clamp and attached the 90o adapter. The 24” support rod was set and the force sensor was place on the 24” rod. Once the force sensor was calibrated, a sequence of masses was suspended from the spring and the amount of stretch was measured and documented in Table 1 as spring 1. The graphing program calculated the slope of the results equaling to the spring constant, Graph 1. This process was duplicated for the second spring (spring 2) and documented in Table 1.

Part A investigated the vertical oscillation of a 0.75kg mass suspended from the spring. The mass was lowered approximately 5cm towards the motion sensor and then gently released. The DataStudio program generated the change in position versus time and Graph 2 displays the results. The results gave a harmonic wave and seven consecutive high points were documented in Table 2.

Part B investigated horizontal oscillation using two springs attached...

...Physics Laboratory Report
Simple HarmonicMotion: Determining the force constant
Aim of experiment:
The objective of this experiment is:
1. To study the simple harmonicmotion of a mass-spring system
2. To estimate the force constant of a spring
Principles involved:
A horizontal or vertical mass-spring system can perform simple harmonicmotion as shown below. If we know the period (T) of themotion and the mass (m), the force constant (k) of the spring can be determined.
[pic]
Consider pulling the mass of a horizontal mass-spring system to an extension x on a table, the mass subjected to a restoring force (F=-kx) stated by Hooke’s Law. If the mass is now released, it will move with acceleration (a) towards the equilibrium position. By Newton’s second law, the force (ma) acting on the mass is equal to the restoring force, i.e.
ma = -kx
a = -(k/m)x -------------------------(1)
As the movement continues, it performs a simple harmonicmotion with angular velocity (ω) and has acceleration (a = -ω2x). By comparing it with equation (1), we have:
ω = √(k/m)
Thus, the period can be represented as follows:
T = 2π/ω
T = 2π x √(m/k)
T2 = (4π2/k) m ---------------------------(2)
From the equation, it can be seen that the period of the simple harmonicmotion is...

...Simple HarmonicMotion
Ethan Albers
Case Western Reserve University, Department of Physics
Cleveland, OH 44106
Abstract:
In this lab, my partner and I observed oscillations that were translational and rotational. The two forms we studied must have a form of a restoring force that is proportional to the displacement of the object from its point of equilibrium. This produces the harmonicmotion which this lab wants. At small and big amplitudes we measured/observed the translational oscillation of the spring. To go with this also, we measured it when it had the spring had added mass and when it didn’t have added mass. Additional to this, we were able to measure the rotational oscillation of a Torsion pendulum that was rotating on its central axis. With this data we created a sine curve to display the oscillating effect which was made possible by using the translational oscillation. After that, my partner and I created a histogram that displayed the different lengths of the period of oscillation. This histogram used the Torsion pendulum to make the graph. In both of these mini labs, they displayed the principle of the oscillating effect that is produced by a restoring force.
Spring Mass Oscillator:
Introduction and Theory:
The way translational harmonicmotion is illustrated is by the oscillation with the spring. The compression and the extension of the spring while it...

...Shanise Hawes
04/04/2012
Simple HarmonicMotion Lab
Introduction:
In this two part lab we sought out to demonstrate simple harmonicmotion by observing the behavior of a spring. For the first part we needed to observe the motion or oscillation of a spring in order to find k, the spring constant; which is commonly described as how stiff the spring is. Using the equation Fs=-kx or, Fs=mg=kx; where Fs is the force of the spring, mg represents mass times gravity, and kx is the spring constant times the distance, we can mathematically isolate for the spring constant k. We can also graph the data collected and the slope of the line will reflect the spring constant. In the second part of the lab we used the equation T=2πmk, where T is the period of the spring. After calculating and graphing the data the x-intercept represented k, the spring constant. The spring constant is technically the measure of elasticity of the spring.
Data:
mass of weight | displacement |
m (kg) | x (m) |
0.1 | 0.12 |
0.2 | 0.24 |
0.3 | 0.36 |
0.4 | 0.48 |
0.5 | 0.60 |
We began the experiment by placing a helical spring on a clamp, creating a “spring system”. We then measured the distance from the bottom of the suspended spring to the floor. Next we placed a 100g weight on the bottom of the spring and then measured the displacement of the spring due to the weight
. We...

...Damped HarmonicMotion
Erica
Partner: Steven
November 8, 2012
Abstract
During this experiment, the effects that the size of an object had on air resistance were observed and determined. To do this, a spring was set up with a circular object hanging at the end. After the spring constant of 9.0312 N/m was measured, equations were used to determine a calculated frequency, that being 7.252 Hz. Four trials—each with a different sized, same massed object—took place where the object was pulled and allowed to rise and fall, while a sonic ranger motion sensor graphed the object’s position. The graphs created were transferred into Igor Pro, where a non-linear fit was created. From this fit, the damping constant of the object’s motion was given, and the effect of air resistance on the object was determined. A relationship was discovered between the object’s area and the effect air resistance had. The results showed that with a greater area of the object, there was more air resistance on the object.
Introduction
The goal of this experiment was to observe the effect that the size of an object had on the air resistance shown when the object was in motion. In order to do this, a damping coefficient was determined through non-linear fits of position graphs produced during its motion. The damping coefficient shows the effect that the damping—air resistance—has on the object, shown...

...examining the simple harmonicmotion of a mass hanging on a spring, three investigations were conducted in the experiment. The experiments include the relation between the period in oscillations and mass, and figuring out if the period vs. mass graph should go through the origin and lastly, finding the mass needed to create a one second timer. It was investigated by placing a motion detector under a spring that was attached to a clamp which was attached to a retort stand. The mass was pushed above its equilibrium and the position vs. time graph was recorded. It was found that it was related by P(s) = 0.04m^0.5, it would take 625 g to make it a 1s timer and the graph would pass through the origin.
Purpose:
When a mass hanging on a spring is raised above the equilibrium position and released, it goes through simple harmonicmotion. This experiment was performed to find the relation between period and mass and to find how much mass would be needed to use this as a 1s timer
The Method
Equipment
The equipment that were used in the experiment are a motion detector, 30 cm rule, a set of mass, computer(LoggerPro), spring, retort stand and clamps.
Procedure
1. A clamp was attached to a retort stand and a spring was hanging from the clamp. The motion detector was placed right underneath the spring. A mass (50g, 70g, 200g, 250g, 400g, and 500g) was attached to the...

...Simple HarmonicMotion Lab Report
In this lab, I will study the principles of simple harmonicmotion using an oscillating pendulum. If I were to design an experiment that would help me study the properties of an oscillating pendulum and investigate what causes a pendulum to swing faster or slower, I would prepare several masses (e.g. 20g, 50g, 100g, 200g, etc.) that can be attached to a string, several strings of varying lengths from 0.1m to 1.0m that are strong enough to support the weight of the masses, support for each pendulum, a stopwatch, and a measuring tool such as a meter stick. Using such materials, I would try to measure the length of the pendulum, the number of cycles the pendulum goes back and forth, the time it takes for the pendulum to do so, and the variables that drive the pendulum to act as so. Based on what I learned in keystone, I would expect to get results that show that the only variable that affects the period of a pendulum is its length. Additionally, that for pendulums swung from angles smaller than 15 degrees, the angle they are swung at are virtually insignificant. If the results were different, there would be a mistake in my recordings or procedure of the results and the experiment because the expected results have already been proven many times over and have been established as official scientific facts.
In this lab, I will measure the period (the time required for the pendulum to...

...Exploration Guide: Uniform Circular Motion
Go to www.explorelearning.com and login. Please type or write your answers on a separate sheet of paper, not squished in the spaces on these pages. When relevant, data collected should be presented in a table.
Objective: To explore the acceleration and force of an object that travels a circular path at constant speed. Motion of this kind is called uniform circular motion.
Part 1: Centripetal Acceleration
1. The Gizmotm shows both a top view and a side view of a puck constrained by a string, traveling a circular path on an air table. Be sure the Gizmo has these settings: radius 8 m, mass 5 kg, and velocity 8 m/s. Then click Play and observe the motion of the puck.
a. The puck in the Gizmo is traveling at a constant speed, but it is NOT traveling at a constant velocity. Explain why.
b. Because the velocity of the puck is changing (because its direction is changing), the puck must be experiencing an acceleration. Click BAR CHART and choose Acceleration from the dropdown menu. Check Show numerical values. The leftmost bar shows the magnitude of the acceleration, or |a|. (The other two bars show the x- and y-components of the acceleration, ax and ay.) What is the value of |a|? Jot this value down, along with radius = 8 m, so that you can refer to it later.
c. Keeping velocity set to 8 m/s, set radius to 4 m. (To quickly set a slider to a value, typing the number...

...THE DATA (PART A)
1. Describe the difference between the two lines on your graph made in Step 6. Explain why the lines are different.
Referring to graph on the right the difference between the two lines is that one line is at a faster speed than the other in the same amount of time. While one is steeper the other one is not as steep.
2. How would the graph change if you walked toward the Motion Detector rather than away from it? Test your answer using theMotion Detector.
Since the graph is going in a positive direction, the guess would be, that the graph would start from the top instead of the bottom, and would go downward causing the direction to become negative.
3. What did you have to do to match the graph you were given in Step 7?
In order to match the graph given in step 7, it had to do with perfect timing, and communication- since the computer screen was not in visible site on the moving person. We had a look at the given graph, interpreted what it said which was: wait for 5 seconds, move in fast motion for 3 more seconds, pause again and at a slower motion keep moving forward and to end pause once more.
4. Sketch a distance vs. time graph for a car that starts slowly, moves down the street, stops at a stop sign, and then starts slowly again.
Time
PROCESSING THE DATA (PART B)
4. Describe the difference between the two lines on the graph made in Step...