### DAMPED PENDULUM COURSEWORK This value also came out to be as expected at 0. I also changed the card shape to circular and I found this to be more aerodynamic as there was less drag due to there being no sharp corners as is the case with the rectangular card and the shape was much more uniform than before. This force of gravity, has two components: Using the above equation, I can see that the decay constant, will be given by the following equation with respect to the amplitude at time, t: Prediction The theory surrounding damping of a spring, is very similar to that for Experiments 2 and 3 see previous theory for details , since the spring is being damped by the affect of air resistance acting upon it. I originally thought this rotation of the card could be caused by either a draft in the room which affected the position of the card or that it was not properly secured to the string. Please note, there are x-axis error bars present on the graph however, due to them being so small in magnitude, they are not easily seen on the graph here. Any errors found in the apparatus or measuring equipment were dealt with appropriately before continuing with the investigation, in order to reduce any possible uncertainties which may arise. Also it is interesting that this logarithmic curve fits the data well since a logarithmic function is the inverse function of an exponential, which is the form of the envelope function when plotting amplitude vs time, as shown in graphs 3. From knowing this, and with the data I had collected, I was able to graph period squared vs length to obtain an equation for my data, where the value of m gradient could be used to calculate a value of accretion due to gravity, g, using my data. As discussed I resolved this issue by weighing each of the masses using an electronic scale to check if the actual value of each mass corresponded with the given value. Additionally I could be due to not taking into account the mass attached to the spring and the spring constant of the spring, because this will have an effect on the period, as per the formula from experiment 4. Percentage Difference between ratios for the These values for percentage difference between Different Diameters are as follows see Table the ratios, show that using smaller diameters, the 3.

You find that the mass stretches the spring by This would not only allow for a more secure fit, as I could simply use plasticine to attach the card to the surface of the mass, but also would be less cumbersome when attaching a new card of different diameter.

## Simple and Damped Harmonic Motion

Despite this subtle difference in the apparatus, as discussed above, the actual method used to obtain the results is identical for both. Part of the reason why the value for half-life may be deemed inaccurate is because I only timed the oscillations for 20 seconds, which meant I have only analysed coyrsework of the motion, and therefore in dajped to gain a more accurate value for k, and thus half-life, I would need to allow the pendulum to oscillate for longer, perhaps two minutes, which would allow not only more data to pendulu collected increasing reliability but also to gain a more accurate assessment of how the amplitude is damped over a longer period of time; since the Graphs 3.

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.

STEPHEN MUGFORD THESIS ASSET MANAGEMENT

The control variables were the same as before, but also include the position of the slow-motion camera, making sure it was always inline with the protractor to gain coursweork easily. However, there seems to be an inaccuracy in my results, since the trend-line does not pass through the origin as expected since these two quantities, force and extension are directly proportional.

The use of this extreme case was necessary in order to confirm that it was the card which was causing this torsional motion a s opposed to any other additional forces acting on the pendulum affecting its motion. To gain a large range of readings, I used a second mass hanger, that I attached to the first one, and then added g masses to this in order to see how much larger masses affect the amount of extension experienced by the spring.

# Damped Oscillation. – GCSE Science – Marked by

Since the ratio for an exponential should be the same or either positive or negative values regardless, I will take the positive number in order to make commenting on the findings and further analysis easier.

During the experiments I conducted, I was swinging a metal weight through a significant distance and peendulum some speed, which may have caused serious injury to someone passing coirsework, if their body had collided with the pendulum bob. 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. From this graph I should be able to see if a relationship exists between the diameter of penvulum used for damping and half-life of the oscillations. Additionally, using a spherical bob would ensure the centre of mass doesn’t change as it would be assumed to be at the centre of the sphere, whereas for the bob I used it was very difficult to determine where the centre of mass was, so I had to make a large assumption that I was at the centre, whereas the fact is, it probably more towards the bottom edge of the mass, which means the forces acting on the bob would be unequal at either end.

Firstly using makeshift compass, I drew a mm diameter circle onto white cardboard which I then drew 5 other concentric circles within: This confirms my prediction that the decrease in diameter of card used for damping, increases the time taken for the amplitude to half, proving that as you decrease the diameter to a negligible size, the pendulum begins to oscillate in exhibiting SHM, in a way that the amplitude remains constant and oscillates between a maximum and minimum value, without decreasing very quickly, to the extent that it takes a longer period of time for the amplitude to decrease exponentially, as shown by the data and the accompanying 42 graphs above.

The tripod was used to mount the camera onto, in order to secure it, and make sure it was positioned in view of the parts setup and also lens was parallel to the protractor to make recording the amplitude easier.

Ramped comfortably secure the card, I used a piece of wooden doweling, which I attached the two string two and then positioned the card on top, making sure to tape the card to the string for extra rigidity. To reduce the random error int his measurement, I took 3 readings, penrulum different orientations in the tube up-down, left-right, diagonal to gain a mean value for the diameter being used.

CUED IIB COURSEWORK COVER SHEET

Figure 12 below, shows the components I used and Figure 13 shows how this apparatus was setup to carry out both sub- experiments. Firstly, since the apparatus used was the same as Experiment 1 with the exception of additional card to the mass as shown in Figure 5, used as the damping mechanism the same errors occurred in the rubbing of the string on the inside of the wooden planks used as the pivot which caused the string to experience additional frictional forces which meant the motion of the pendulum was not damepd straight back and forth, Figure 8 left: As you will see, I pendjlum not include anomalous results, because despite the errors which occurred during this experiment, the actual data I recorded was all fairly consistent for each of the 3 measurements taken.

# Simple and Damped Harmonic Motion – UBC Wiki

Because Pendu,um measured a large number of cycles, he thought that this law held true for larger angles too.

This article is part of the PhysicsHelp Tutoring Wiki. In light of this conclusion, he began to use the pendulum to measure short time periods. I also plotted the point 0,0 on this graph to see how much difference the value of damled would be if the graph did, as expected, start at the origin.

Therefore, the independent variable was the force applied, which was changed by adding more mass each time to spring using the attached mass hanger. In the future, this calibration should be done beforehand and the camera setup in position prior to recording in order to save valuable time.

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

However to minimise the risk of additional anomalies through the use of a new pivot, which reduces additional damping, I used this same apparatus with the additional of tape and plasticine to hold to the string in place between the two planks of wood. In real systems, masses on springs don’t continue to oscillate forever at the same amplitude; eventually the oscillations die away and the object stops.

I would say this is due mm: Secondly, I tested how the period for 10 complete oscillations changes as more mass is added to the spring. To find this, I positioned the ruler inline with the coil on the spring as shown and measured the piston of the last coil on the spring using the ruler, which I recorded as x0the equilibrium position. Both ends of the tube were carefully adjusted to make sure the diameters were 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.

I would suggest this may be due to a systematic error in observing when 20 oscillations are complete, which meant I stopped the stopwatch too early, so the value for period was lower than expected. Surprisingly, this time came out to be approximately It also agrees with my through the origin as the percentage error for predictions, proving my initial ideas to be true.