# DAMPED PENDULUM COURSEWORK

This procedure of measuring the new diameter, then measuring the maximum amplitude reached after 20 complete oscillations was repeated for 3 different diameters of the tube, then the same procedure repeated for a closed-ended tube, where the bottom end of the tube was simply covered over by a piece of circular cardboard to see how my results differed between an open and closed ended tube. In order to clarify whether the value for the spring constant I found here is accurate I needed to produce a graph for the data collected using the second method to see how this compares. To further reduce any random error, I took 3 separate measurements of length for each piece of string and obtained an average value which as expected came out to be 0. The independent variable was the diameter of tube which I changed each time to get 4 different diameters from which to gain different results. This is a very simple case. As discussed previously, this was most likely due to an angled rather than straight release of the mass.

Therefore, the independent variable was the force applied, which was changed by adding more mass each time to spring using the attached mass hanger. This was the characteristic equation of damped harmonic motion, and the one which I used to obtain the values for the decay constant and half life of each set of data. One night you suspend the spring from the ceiling in your room and hang the mass from it. Therefore care had to be taken not to overload the spring and stretch it beyond its elastic limit. I decided upon using rectangular card, as I felt it would have a substantial effect on the damping of the pendulum — indeed it did, however the motion of the pendulum was no longer straight back and forth as before, it was now slightly elliptical which meant the period of the damped motion was slightly longer than the undamped case in experiment 1, whereas theory states that since the period is unaffected by the amplitude, any change in the amplitude should not affect the value for period of an oscillation. But this velocity is positive, and we were told that the object is travelling downwards.

Here, the peneulum variable was the mass added on the end of the spring, which was being changed. The measuring cylinder was used to contain cm3 of water and allow the mass to oscillate vertically in the water in order to record the amplitude of the spring after 20 complete oscillations.

These measurements of the diameter of the tube were taken prior to taking the next set of results, due to the diameter having to be altered to obtain a wide range of results.

As shown in Figure 14 above, the tube was attached to the ruler in order to make it completely secure. Given Equation 8, as proposed in the initial theory for my research, it states that: This is much smaller of an error than was found for the mm2 card which shows that perhaps due to having the largest amount of additional air resistance, the values for amplitude which I recorded had a high level of inaccuracy and therefore, the error in the ratio of these values would be much higher.

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The general trend of the line fits the data extremely well with an R2 value of 0. I also plotted the point 0,0 on this graph to see how much difference the value of g would be if the graph did, as expected, start at the dsmped.

## Damped Oscillation.

These anomalous results, were taken as such and then repeated to obtain a more accurate value and therefore these anomalous values were disregarded in couursework calculation of a mean and instead used the improved values, which were closer to the other two recorded data points.

To find this, I positioned the ruler inline with the coil on the spring as shown and measured the piston of courseqork last coil on the spring using the ruler, which I recorded as x0the equilibrium dampfd.

We know that when the mass is at rest at My second experiment involved the same setup as before, just the add-on of rectangular pieces cardboard of different areas attached to the string using holes in the centre of the card.

Firstly, I tested the force applied to the spring against its extension.

# Damped Oscillation. – GCSE Science – Marked by

By testing at this extreme, I was able to obtain solid, conclusive evidence that it was the torsional motion which affected the readings in my experiment. Prediction Since this experiment is an improvement on Experiment 2, the actual quantities being measured remained the same. The pendulum is assembled from a string or a light rod with a weight at one end.

Using this equation I inputted the values for k, that I found above. This article is part of the PhysicsHelp Tutoring Wiki. The time coursewofk for the pendulum to move from its most extreme right position coursfwork to that point.

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

Therefore I used ordinary woollen string, as opposed to suggested nylon string, despite the nylon string being much thinner and smoother which would reduce the friction and air resistance of the string in motion and thus would give greater accuracy in results.

To check the time taken was approximately 20 seconds, as expected, I used the orange stopwatch as used previously to record the time taken for 20 penndulum oscillations to occur.

The closer to 1 this value is, the more well correlated the points are to the line of best fit. Finally, as shown, the rectangular card was threaded through two holes to attach it to the string and then taped using duct tape at these two points, to secure the card in place in order to recede any rotation of the card during motion. Stopwatch – The stopwatch was used to measure timings for different parts of my investigation. Note that this value for m e-spring is not the actual mass of y-intercept 0.

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I found that a logarithmic line fitted the data points quite well as shown below, which allowed me obtain an equation for the curve in order to complete further analysis into the relationship between diameter of card and half-life.

From this, the equation states that: Then the term, k, in the bracket represents the pendjlum constant of the exponential which is the value I will use later on to calculate the half life of each different diameter used.

Therefore the maximum 5. I had thought about also plotting graph of these values danped half-life vs the area of card, however since there are only 3 different areas of card, the relationship between he variables would not be easily seen from the graph plot.

I performed the same calculation for the same 3 points, using the data collected for the other 2 areas of card that I tested. Once this was complete this could then lead me to investigate other factors which affect the motion of the pendulum and a spring such as damping, in both air and water. 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 a 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.

For each experiment, I shall outline the variables involved prior to discussing the methodology. Additionally all measurements of the extension were made at eye-level with the ruler in order to reduce parallax error in the readings of the markings on the ruler.