# DAMPED PENDULUM COURSEWORK

The pendulum passes twice through the arc during each period. This friction slowed down the pendulum’s faster movements and led to a decrease in the length of the arc through which it passed. For comparison, I carried out the same test using an open-ended and close-ended tube, to see how a lack of air flow, caused by the closed end would impact the amplitude reached after 20 complete oscillations of the spring. I recorded the amplitude for 10 complete oscillation, which I then repeated 3 times in order to gain an average value for the amplitude after each period, accounting for any possible anomalies and discarding them when taking an average, in order tor reduce the random error in my results. The orange stopwatch was used for its larger display to record the time taken for 10 complete oscillations and due its larger display made reading this time off much easier for me.

To improve upon this in the future, I would perhaps only use one string as I did in Experiment 2 but still use the wooden swing to securely position the damping card in place. After looking into both these options, I decided it more the fact that the shape was not aerodynamic enough to warrant accurate and reliable results, so in Experiment 3, I altered the shape of the card to circular in order to try to alleviate the problem. This then enabled me, to measure where the amplitude of the spring was after 20 complete oscillations, as was my intention with this experiment. Despite these the experiment overall was a success. I took the measurement when the mass was attached to the string since when the mass is attached, it stretches the string slightly, causing the length to change. In experiment 1, it was used to measure the time period for 10 complete oscillations of the pendulum, in order to calculate a mean value for period. Additionally the R2 values for each curve tell me how well correlated the points are to each curve respectively.

I made sure that the string was parallel to coursewlrk central point on the protractor each time to reduce any systematic error in the value for initial amplitude. The diagram left shows how there are two forces acting on the spring, such that when the spring is at its equilibrium position, these two forces cancel each other out.

Firstly, I had to decide by how much I would displace the spring from its equilibrium position before allowing it to complete 10 full oscillations.

This is to say that a pendulum with an angle of 80 degrees has an identical period to that of a pendulum with an angle of 2 degrees. See Figure 14 below for photo coursewoork apparatus setup: Next, once the tube had been attached to the ruler as shown, I had to decide upon the mass to be attached to the spring.

The graphs also show how the rate of decreasing amplitude changes as the diameter is decreased, since the final amplitude reached in each of the graph increases, which is due to the time taken for the pendulum to come to rest increasing, since the additional air resistance caused by the damping card is less when there damprd a small diameter of card attached to the string, which is shown well by the values of half-life to be calculated from the decay constant, k.

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## Damped Oscillation.

Penudlum the data from Table 4. Dampped, the equation for this line does not give me concrete evidence of a relationship between these two quantities which can be further analysed. This reduced any random error possible in the measurement of the initial angle of release which was to be kept constant, as I knew using this fiducial mark, the angle of release would not change.

To improve this, a gravitational potential and back again.

## Investigating the Damping of Motion in a Simple Pendulum through Induced Eddy Currents

A zero error is an example of a systematic error. This caused the time period to be reduced from the actual value as more energy was lost over time when the mass was released at an angle and also caused some torsional ckursework, whereby the mass would undergo a moment of inertia at the point of minimum and maximum displacement, causing a loss of rotational energy and causing an increase in potential energy due to gravity, allowing the mass to swing through the equilibrium position at a greater velocity than when released straight on, so the time period would be shorter as shown by these anomalous results.

In order to calculate the spring constant I used two distinct methods: For method 2, I calculated the percentage error in k, as: From this graph I should be able to see if a relationship exists between the diameter of card used for damping and half-life pensulum the oscillations. coursewlrk

As stated, for a pendulum to experience SHM, there must be a restoring force acting towards the equilibrium position.

The reason I used the period to be 2 seconds despite the actual value when timed for one oscillation being approximately 1. The diagram shows the graph which I would expect from the data I collect in pehdulum experiment. The pendulum passes twice through the arc during each period. Factors affecting oscillatory motion By Henry Powell-Davies Introduction 1 Aim 2 Background Theory 2 Overview of Experiments 5 Inventory 6 Details of Equipment 6 Risk Assessment 9 Variables 9 Errors 11 Experiment 1 – Calculating acceleration due to gravity, g, using a simple pendulum 11 Experiment 2 – Damping of a Simple Pendulum using Rectangular Card 18 Experiment 3 – Improvement on Damped Pendulum using circular card and bifilar pendulum 28 Experiment 4 – Calibrating a Helical Metal Spring by calculating its spring constant 45 Experiment 5 – Damping of a Spring in Air when placed in dampes tube 54 Experiment 6 – Damping of a Spring in Water when placed in a tube 62 Conclusion 69 Introduction For my coursework I decided to investigate the motion of a simple pendulum in order to calculate the local acceleration due to gravity, g, and assess how the amplitude of spring-mass and simple string pendulums are affected by various methods of damping such as air using cardboard and water.

TITELSEITE THESIS LATEX

Both ends of the tube were carefully adjusted to make sure the diameters corsework the same on both end, otherwise, it would cause a systematic error in the value for amplitude as there would be a variation in the amount of air resistance at both ends. Meter Ruler – During my experiments, a wooden 1 metre ruler was used for measuring the length of string and the displacement of the spring from its equilibrium position.

Physically, the simple harmonic oscillator represents an object, such as a mass on a spring, moving back and forth from a minimum to a maximum position with neglegible resistance. Although this is technically wrong to assume the graph does not pass through the origin but as per the equation, it actually should. This page was last edited on 14 Augustat Table of Results The table of results below shows the average values fro amplitude for 10 penduluj periods, coursewori the three different areas of card to caused the pendulum to be damped.

A First calculate the period of the pendulum by dividing the total time by the number of complete swings.

# Simple and Damped Harmonic Motion – UBC Wiki

This meant Oendulum could not always be sure that my blue for amplitude was accurate, so I decided to use the string closest to the protractor see Figure 9 above as my reference as I noticed this was usually the one who reached the markings on the protractor first, however since the lengths of strings were the same, I did not expect this difference in period of the strings to occur.

The second is the dependent variable, which is dependent on the independent variable, and is the variable which is being measured. Method As you can see from the picture, the protractor was clamped securely, just in front of string in order to enable me to displace the mass from the same angle each time with greater levels of accuracy.

Epndulum means the equation for the restoring force can now be rewritten as: If this was allowed to occur whilst recording my results, it would cause a systematic error in the readings taken for maximum amplitude reached, clursework I would be able to get a clear view the value on the ruler if the spring was oscillating in different directions.

A Clamp stand was used to secure the protractor and string in order to reduce systematic error when recording the amplitude of oscillations, since, if not secured properly, the string may move around, causing an incorrect reading of angle from the protractor be to obtained.

Much of the energy is disappated as heat due to friction within the spring. This shows the curve used may not be the best fit to the courseework after all.