1142 Words5 Pages

This report investigates resonance phenomena of driven damped simple harmonic oscillations by measuring accelerations and frequencies of an oscillator. Since it turned out that oscillations with low damping have smaller errors than those with high damping, small damping cases are employed to examine the resonance phenomena. Based on the Newton's 2nd Law \cite{book}, the motion of oscillations can be modeled by the following differential equation and its solution.

\begin{equation} \label{eq1}

\ddot x+2\gamma \dot x+\omega_{0}^{2} x=\left(\frac{F_{0}}{m}\right)e^{i\omega t}

\end{equation}

\begin{equation} \label{eq2} x(\omega)=\frac{F_{0}/m}{\omega_{0}^{2}-\omega^{2}+2i\gamma\omega}=A(\omega)cos(\omega t-\phi)

\end{equation}

Acceleration*…show more content…*

In total, 16 experimental data points have been taken after settling to each steady-state for various driven frequencies. The voltage data obtained in Lab View is then converted to the acceleration data by multiplying its amplitudes by the slope of the two calibration points. Here, the voltage data is calibrated with gravity only and with no acceleration. The slope is called calibration factor. Errors for accelerations are the calibration factor times the error of the cursor measurements of Lab View, and that is the minimum difference Lab View can measure. Errors for the phase shifts are obtained by equation \ref{eq5} where \(\Delta f¥\) is an error for the driven frequency derived from the variation in frequency displayed on the oscilloscope \cite{oscilloscope}, \(t\) is a time shift between the peak of the acceleration of the oscillator and the driven force, \(\Delta t\) is an error for the time derived from the grid square size in the Lab View waveform graph.

\begin{equation} \label{eq5}

\Delta \phi = \phi \sqrt{(\frac{\Delta f}{f})^{2}+(\frac{\Delta t}{t})^{2}}

\end{equation}

At the beginning of the experiment, the natural frequency of the oscillator with neither the eddy currents nor driving force is observed as \(\omega_{0} = 75.7 \pm 0.1 \) rad/s or equivalently \(f_{0} = 12.05 \pm 0.01 \) Hz.

The result of the experiment is summarized in Figure ~\ref{fg:A} and ~\ref{fg:AandPhi}. The overall

\begin{equation} \label{eq1}

\ddot x+2\gamma \dot x+\omega_{0}^{2} x=\left(\frac{F_{0}}{m}\right)e^{i\omega t}

\end{equation}

\begin{equation} \label{eq2} x(\omega)=\frac{F_{0}/m}{\omega_{0}^{2}-\omega^{2}+2i\gamma\omega}=A(\omega)cos(\omega t-\phi)

\end{equation}

Acceleration

In total, 16 experimental data points have been taken after settling to each steady-state for various driven frequencies. The voltage data obtained in Lab View is then converted to the acceleration data by multiplying its amplitudes by the slope of the two calibration points. Here, the voltage data is calibrated with gravity only and with no acceleration. The slope is called calibration factor. Errors for accelerations are the calibration factor times the error of the cursor measurements of Lab View, and that is the minimum difference Lab View can measure. Errors for the phase shifts are obtained by equation \ref{eq5} where \(\Delta f¥\) is an error for the driven frequency derived from the variation in frequency displayed on the oscilloscope \cite{oscilloscope}, \(t\) is a time shift between the peak of the acceleration of the oscillator and the driven force, \(\Delta t\) is an error for the time derived from the grid square size in the Lab View waveform graph.

\begin{equation} \label{eq5}

\Delta \phi = \phi \sqrt{(\frac{\Delta f}{f})^{2}+(\frac{\Delta t}{t})^{2}}

\end{equation}

At the beginning of the experiment, the natural frequency of the oscillator with neither the eddy currents nor driving force is observed as \(\omega_{0} = 75.7 \pm 0.1 \) rad/s or equivalently \(f_{0} = 12.05 \pm 0.01 \) Hz.

The result of the experiment is summarized in Figure ~\ref{fg:A} and ~\ref{fg:AandPhi}. The overall

Related

## How Did Takaaki Kajita Got The Nobel Physics Prize

1520 Words | 7 PagesPhilosophy Prize. But there's also a Nobel Physics prize, In 2015 A man named Takaaki Kajita won that prize with Arthur B. McDonald. Ever since 1901 people have been able to win a Nobel Physics prize and only 111 people have ever won one! You must be thinking, How did Takaaki Kajita get his hands on one? Well, it’s clearly Not easy he was 55 when he got it! Well In this essay Not only are you gonna learn just exactly how Takaaki Kajita got the Nobel Physics prize but about his background in the process

## Reaction Paper On Bungee Jumping

3212 Words | 13 Pages￼FINAL Dante Mattson 11 Physics 28 August 2014 ! Bungee Jumping is an extreme sport, it requires the participant to jump from a bridge, crane or other high place while secured at the ankles with a nylon-cased rubber band. From the mere sight of someone Bungee Jumping, one might assume that the act is very dangerous for obvious reasons, for example: The rope breaking - there’s nothing to save you down there, so why do so many people put their lives in a piece of elastic? Bungee Jumping relies on the

## Neutrino Research Paper

683 Words | 3 Pagesnot only address the importance of these tiny particles, but in addition to the interesting history behind the discoveries of the various characteristics, what that means for modern science, and the future of neutrino and theoretical physics research. In nuclear physics, there are various types

## Edexcel AS Physics in 100 pages

19416 Words | 78 PagesEdexcel AS Physics in 100 Pages -----an easy-to-understand textbook & exam preparation guide Copyright ©2011 by Yajun Wei All rights reserved under international Copyright Conventions. No part of the text of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without permission in writing by the publisher, except by reviewers or catalogues not limited to online for purpose of promotion. Front Cover photo

## Year 11 Physics Assignment

2811 Words | 12 PagesNotice of Assessment Task Preliminary Course in Physics Date of Initial notification: 1/2/2013 | Date of submissionTerm 1 Week 5 | Task Number: One – Research | Time Allowed:2 weeks | Weighting of Task: 15% | Course component / Focus area / Topic Module:Module1: The World Communicates | Task Description:The world communicates by making extensive use of the electromagnetic spectrum. For the average person this is commonly accessed using radio waves. These radio waves may be over the

## Self-Assessments In Physics

610 Words | 3 PagesAfter the first 10 minutes of class on the first day of school we were told that we are going to have to figure things out by ourselves and that the teacher will encourage self learning. I learned that physics class is going to be like a research lab where you are only given very little information and the rest you are going to have to come up by yourself. Another example of this is when we had to create a lab by ourselves. Although we did do this for one lab last year in 8th grade it was a different

## Hooke 's Law And Simple Harmonic Oscillations

1085 Words | 5 PagesCollege physics II Laboratory Experiment 2 “Hooke 's law and simple harmonic oscillations” by Mohamed Omer Lab Partners Youssef Farlos Roman Martinaz Jhon Fanque Date performed January 18, 2015 Introduction/ Abstract: Simple harmonic motion is the study of oscillation. An object undergoes oscillation when it experiences a restoring force which restores this object to equilibrium positon. The

## Taking a Look at DNA Supercoiling

684 Words | 3 Pagesin the right direction; whereas negative supercoiling means that the DNA strands are twisted in the left direction. The laws of Physics govern everything that happens in the world, including DNA coiling in living beings. Some of the concepts in Physics that are involved in DNA coiling are quantum mechanics and statistical mechanics. Quantum physics is a branch of physics that explores certain units of energy, which are called quanta. These units of energy are described by the Quantum Theory. The

## Purpose Statement For Purpose In Physics

1787 Words | 8 Pagesmaster of Science in physics at Sardar patel University. Bearing in mind my academic background, capabilities and interests, I had decided to pursue graduate studies in physics with my focus on CONDENSED MATTER PHYSICS AND MATERIAL SCIENCE. In what follows, I have briefly summed up my motivation for the graduate study, my back ground and my research interest. Right from the onset of my academic years, fascination for the physics and mathematics had promoted me to do a major in physics. I started my education

## Otto Robert Frisch Essay

1348 Words | 6 PagesRobert Frisch was born in Vienna, Austria on October 1st, 1904 to Justinian and Auguste Meitner Frisch. His father and mother were a painter and a concert pianist, respectively. Frisch’s aunt was Lisa Meitner, a physicist. Otto shared her love of physics and would later work with her and make an important discovery that was essential to the creation of the atomic bomb. Frisch came from a Jewish family, so when Adolf Hitler rose to power and started persecuting the Jews, it had a direct impact on

### How Did Takaaki Kajita Got The Nobel Physics Prize

1520 Words | 7 Pages### Reaction Paper On Bungee Jumping

3212 Words | 13 Pages### Neutrino Research Paper

683 Words | 3 Pages### Edexcel AS Physics in 100 pages

19416 Words | 78 Pages### Year 11 Physics Assignment

2811 Words | 12 Pages### Self-Assessments In Physics

610 Words | 3 Pages### Hooke 's Law And Simple Harmonic Oscillations

1085 Words | 5 Pages### Taking a Look at DNA Supercoiling

684 Words | 3 Pages### Purpose Statement For Purpose In Physics

1787 Words | 8 Pages### Otto Robert Frisch Essay

1348 Words | 6 Pages