The Introduction
Abstract
Through examining the simple harmonic motion 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 harmonic motion. 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 end of the spring. It was made sure the mass was at least 20 cm above the motion detector. 2. The mass was raised above the equilibrium to start the simple harmonic motion, and then the motion detector generated a position vs. time graph on loggerpro. 3. Then the mass was changed and the steps were recorded until there were 6 positions vs. time graphs of 6 different masses. Data

Mass( ±1 g)| Period ( ± 0.01 s)|
250| 0.58|
50| 0.26|
200| 0.50|
500| 0.80|
70| 0.3|
400| 0.75|
Table1: Period of oscillation (s) for various...

...SimpleHarmonicMotion
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...

...EXPERIMENT 2 Measurement of g: Use of a simple pendulum
OBJECTIVE: To measure the acceleration due to gravity using a simple pendulum.
Textbook reference: pp10-15
INTRODUCTION:
Many things in nature wiggle in a periodic fashion. That is, they vibrate. One such example is a simple pendulum. If we suspend a mass at the end of a piece of string, we have a simple pendulum. Here, the to and fro motion represents a periodic motion used in times past to control the motion of grandfather and cuckoo clocks. Such oscillatory motion is called simpleharmonicmotion. It was Galileo who first observed that the time a pendulum takes to swing back and forth through small distances depends only on the length of the pendulum The time of this to and fro motion, called the period, does not depend on the mass of the pendulum or on the size of the arc through which it swings. Another factor involved in the period of motion is, the acceleration due to gravity (g), which on the earth is 9.8 m/s2. It follows then that a long pendulum has a greater period than a shorter pendulum.
Before coming to lab, you should visit the following web site: http://www.myphysicslab.com/pendulum1.html This simulation shows a simple pendulum operating under gravity. For small oscillations the pendulum is linear,...

...Shanise Hawes
04/04/2012
SimpleHarmonicMotion Lab
Introduction:
In this two part lab we sought out to demonstrate simpleharmonicmotion 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...

...Physics Laboratory Report
SimpleHarmonicMotion: Determining the force constant
Aim of experiment:
The objective of this experiment is:
1. To study the simpleharmonicmotion 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 simpleharmonicmotion as shown below. If we know the period (T) of the motion 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 simpleharmonicmotion 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...

...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...

...Simple Pendulum
PURPOSE
The purpose of this experiment is to study how the period of a pendulum depends on length, mass, and amplitude of the swing.
THEORY
A simple pendulum is an idealized model consisting of a point mass (sometimes called a pendulum bob) suspended by a massless unstretchable string. When the bob is pulled to one side of its straight down equilibrium position and released, it oscillates about the equilibrium position. The path of the bob is not a straight line but an arc of a circle with radius L equal to the length of the string. We use as our coordinate the distance x measured along the arc. If the motion is simpleharmonic, the restoring force must be directly proportional to x or to θ because x=L θ. The restoring force F is the tangential component of the gravity. The restoring force is proportional not to θ but sin θ, so the motion is not simpleharmonic. However, if the angle θ is small, sin θ is very nearly equal to θ (in radians). Thus we have:
The bob will then execute simpleharmonicmotion and x (or θ) will be a sinusoidal function of time:
Where A, called the amplitude, is the maximum value of θ (i.e., A=θmax, or the value of θ when the bob is released to t=0) and the angular frequency is given by
The period (the time for one complete oscillation) is then:...

...Lab Report - The Simple Pendulum
Name: XXXXXXX XXXXX XXXXXXX
Date: January 18, 2013
Objective:
Gain insight on how scientists come to understand natural phenomena through theoretical and experimental data by determining the Period of a Simple Pendulum. This experiment will introduce us to the processes of data collection and the procedures used for data /error analysis.
Theory:
A Period of motion is a physical quantity associated with any cyclical natural phenomenon and is defined as one complete cycle of motion. There are many examples of this in nature, such as the earth’s period of rotation around the sun takes approximately 365 days.
The Simple Pendulum is a basic time-keeping apparatus. A weight is suspended on a length of string which in turn is attached to a frictionless pivot so it can swing freely. The time period it takes to complete one swing is determined by the theoretical equation derived from the Physical Theory of Repeating Motions, aka SimpleHarmonicMotion.
T=2π〖[L⁄g]〗^(1/2)
Where T is the period, L is the length of the pendulum and g is the acceleration due to gravity,
g=9.81 m/s^2.
Once finding the theoretical period we when can compare it to experimental measured value we found of the period. In gathering the experimental data there will be a degree of uncertainty associated with the gathered...

...Goals
The purpose of the lab experiment is to explore simpleharmonicmotion (SHM). We will accomplish this through the validation of harmonic calculations and ultimately creating a time piece (oscillator)
Method
In part A (Simple Pendulum) we will measure the effects of mass on the period of the pendulum. We will also calculate the period using small angular displacements and compare the results. We will also explore the effects on the period when the angular displacement is not “very small” (in essence > 10°). Lastly we will look at creating our own pendulum clock to create a period of 1 second.
In part B (Mass on a Spring) we will experiment with oscillations of a spring. We will then estimate the spring constant. Based on the spring constant we will then calculate the mass need to create a period of 1 second with our spring.
In Part C (Physical Pendulum) we will determine gravity within the classroom.
Figure 1: Pendulum with photogate
Figure 2: Hanging mass on Spring
Figure 3: Physical Pendulum
Data and Results
Part A: Simple Pendulum
First we set up a pendulum with a hanging mass suspended from it. The pendulum moving through a small angular displacement passes through a photogate which is recorded and then averaged below
m = 100 g = 0.1 kg
Pendulum Width = .022 m
Θ < 10° (Small angular displacement)
L = 0.71 m
Table 1: Measured...