I used a stopwatch, with a large, clear display which made reading off a value for time very quick, efficient and easy. As predicted at the beginning of this experiment, I believe the half life will be greater for smaller diameters of card. The time taken to make one complete oscillation is defined as the period, T. I found out the following: Therefore, any anomalies were discarded when calculating the mean values for amplitude at each point in order to obtain the most accurate and reliable results possible, from the data I had collected. It also agrees with my through the origin as the percentage error for predictions, proving my initial ideas to be true.

Since the angular frequency is defined as: When releasing the mass, I did so with care and skill to make sure I did not exert any additional force onto the mass which could impede the motion of the pendulum, causing an error in my readings for period. Despite these the experiment overall was a success. One night you suspend the spring from the ceiling in your room and hang the mass from it. A zero error is an example of a systematic error.

To check the points obeyed an exponential relationship, I divided the 1st value by the 2nd and so on for several values to check if the ratio is constant, as should be the case for an exponential relationship.

damped pendulum coursework

From the equation given for the trend-line, you can see that the value given for the spring constant: From this I can obtain the following equation to calculate k. Then the term, k, in the bracket represents the decay constant of the exponential which is the value I will use later on to calculate the half life of each different diameter used. The only anomalous result I recorded was as shown in Table 4.

Courseqork average values are what I have included in my results table for this experiment as you will see later on.

damped pendulum coursework

Simple harmonic motion is defined as an oscillation in which the acceleration of pebdulum object is directly proportional to its displacement.

In the future, this calibration should be done beforehand and the camera setup in position prior to recording in order to save valuable time. The reason I used the period to be 2 seconds despite the actual value when timed for one oscillation being approximately 1.

This risk assessment spans all courseork experiment I conducted and takes into account any parts which could cause harm or injury to people whilst taking place. When I weighed the spring before starting the experiment, I found the mass of the spring to be The control variables were: Taking more than one reading may reduce this error since it would account for any anomalies readings caused by parallax or oscillating o the spring whilst taking a reading.


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. If the pendulum is set in motion, so that it swings back and forth, its motion is said to be periodic.

One of the main sources of errors in this coursweork was in measuring the amplitude reached during successive oscillations.

Simple and Damped Harmonic Motion – UBC Wiki

Refer to Graphs 4. This allowed me to be more confident in the plots being accurate since the average value accounts for any anomalous results, which I discarded if found, and thus reduces the random error in the value for k which I obtain, as it will actually be the average value for k, coursewofk the decay constant. Due to there being a penxulum rotten end on one end of the ruler used, I decided to measure the length from 1 cm in on the ruler which required care and precision to obtain results which were both consistent and accurate to the true value of length of the string.

However, after doing some plenary work using these shorter lengths, I found the period of an oscillation was far too quick to be easily observed by the naked eye. The closer to 1 this value is, the more well correlated the points are to the line of best fit.

However, the value for g as calculated in the caption below is equal to 9. In the future I would test a variety of springs with different spring constants, in pendu,um to decide on the spring which would allow me to gain the widest range of data possible, as my results were limited to an added mass of only g total, which in hindsight did not affect the spring much, and it was fairly stable when this amount of mass was attached, so I could have gone beyond g to perhaps 1 kg, in order to gain a wider set of data and thus a more precise value for the spring constant at larger loads.

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

Also to mention, the slow-motion camera, is positioned out of shot on the tripod and is facing the protractor so the display can see the markings on the protractor in order for me to measure the amplitude at the given times using the footage captured from the camera. Due to this limitation in using smaller masses, I decided upon g as the mass to be attached to the end of the spring, as this meant the spring would exert minimal resonance, making the values for amplitude which I record much more accurate, and less prone to be incorrect due to the systematic error associated with resonance motion of a spring.


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. Again to reduce random error in the value for length, I took 3 measurements of each length and obtained a mean length for each different length of string.

Now using circular card, the diameter of card, is what I will change, so this will be the independent variable.

Damped Oscillation.

Errors and Improvements Despite the care I took in setting up the penculum and calibrating the equipment prior to beginning this experiment, there were several errors which have greatly affected the reliability of my results, hence why I sought to improve upon the experiment in the best way possible.

Variables There are 3 types of variable. Prior to beginning the experiment, I weighed the mass, using an electronic scale. I would expect this error is due to inaccurate measurement of the equilibrium position due to continuous oscillation of the spring making it hard to determine exactly where the equilibrium position lies, which means there is an error incurred in each of the points, causing the trend-line to be slightly out.

Since this damping term acts in the opposite direction of motion and is proportional to velocity, it causes objects with dampee vlocity to slow down quickly. An additional control variable suing this improved setup, is the position of card above the mass, using the coudsework swing to sit the card on. Firstly, I tested the force applied to the spring against its extension. As the apparatus had been calibrated and setup in dxmped previous sub-experiment, I could simply reposition the spring to make sure the coils were easily visible in front of the ruler as shown in Figure 13 before to collect the data.

This way, I could be sure coursewogk the two strings would travel along the same trajectory and therefore reach the same point at the same time, thus reducing any possible systematic error in the amplitude measurement.