Our academic experts are ready and waiting to assist with any writing project you may have. Note that the angular amplitude does not appear in the expression for the period. In this report, we will replicate their experiment, and will find an accurate value for ‘g’.
THE SIMPLE PENDULUM DERIVING THE EQUATION OF MOTION The simple pendulum is formed of a light, stiff, inextensible rod of length l with a bob of mass m.Its position with respect to time t can be described merely by the angle q (measured against a reference … I've no problem to arrive this result and formula. Study for free with our range of university lectures! Alternatively, measuring the time for 20 swings, instead of 10 swings, would also reduce the uncertainty in time. Depending on the degree of damping, it may or may not have a significant effect on our measurements. I've just studied simple pendulum: The simple pendulum (for small oscillations) differential equation is first image.
This resulted in an uncertainty in length that was higher than one would normally expect. The governing equation of motion of the pendulum is given by ö +25W,+we (1) L Plot the angular displacement ratio eL/X, as a function of frequency ration and damping ratio Take frequency ratio 0 - 3 and damping ratio 0.05,0.10,0.15, and0.20 x(t) = X, eiwit Се L m O Figure 2: Pendulum with Base Excitation, mechanical engineering questions and answers. Apart from these measurements, one more experiment was done to see how much damping was present in our set-up. The suggested square-root relationship shows it, and to linearise this curve, it must be interchanged and the axis must be modified. Furthermore, to find an accurate value for ‘g’, we will also graph T2 versus the length (l) of the pendulum.
While drawing the graph for the data in table 2, the relationship between the variables used is clearly not a linear one. All work is written to order. If you need assistance with writing your essay, our professional essay writing service is here to help! We measure it in seconds. The dimensions of this quantity is a unit of time, such as seconds, hours or days. The actual line of best fit does not go through (0,0) which suggests a systematic error in our experiment. The time period is given by, T = 1/f = 2π(L/g) 1/2. For this investigation, limited resources like, clamps, stands, a metre ruler, a stopwatch, a metal ball (bob), and some string were used.
From simple essay plans, through to full dissertations, you can guarantee we have a service perfectly matched to your needs. Simple pendulum formula Consider the bob at the position B during its vibratory motion as shown in figure.Let ‘m’ be the mass of the bob and x be the displacement of the bob from the mean position at position B.There are two forces are acting on the bob at this position. √ is the square root of what is included in the parentheses 4. Copyright © 2003 - 2020 - UKEssays is a trading name of All Answers Ltd, a company registered in England and Wales.
In this experiment, it looks as if we systematically used a length for the pendulum that was too short. A pendulum is an object consisting of a mass suspended from a pivot so that it can swing freely. In table 1 the ±o.46 sec uncertainty in time was obtained by comparing the spread for the different measurements. To export a reference to this article please select a referencing stye below: If you are the original writer of this essay and no longer wish to have your work published on the UKDiss.com website then please: Our academic writing and marking services can help you! Privacy Find here the period of oscillation equation for calculating the time period of a simple pendulum. My problem is to get to the second formula by passing through another formula (Image 3) that my book mentions.
All measurements were taken under the same conditions, using the same metal bob, the same ruler, in the same room, and at approximately 26 degrees Celsius. Physics No plagiarism, guaranteed! The theoretical value used, is the average value for ‘g’ on Earth, and may be slightly different from the one that was measured. Secondly, the time for one swing (or one period) must be found, which will reduce our absolute error, but not our percentage error. iii, Figure 1 – Set up of simple pendulum experiment …………………………………. & The only things that affect the period of a simple pendulum are its length and the acceleration due to gravity. But when graphing a line of best fit, with the condition it should pass through (0,0), we find a line with a gradient of 4.128 and a correlation coefficient of 0.993, which further suggests a very strong linear correlation between our chosen variables. The differential equation given above is not easily solved, and there is no solution that can be written in terms of elementary functions. One added difficulty in determining the length of the pendulum was the relative big uncertainty in finding the exact length, since the metal bob added less than a centimeter to our string length, measured from the bob’s centre.
Registered office: Venture House, Cross Street, Arnold, Nottingham, Nottinghamshire, NG5 7PJ. A simple pendulum consists of a mass m hanging from a string of length L and fixed at a pivot point P. When displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion.