A simple Pendulum Essay Example

A simple Pendulum Essay My aim in this experiment was to see if the length of the string the bob was attached to effected the time taken for one oscillation.RESEARCHWhat a pendulum is:A pendulum is a body suspended by a fixed point so it can swing back and forth under the influence of gravity. Pendulums are frequently used in clocks because the interval of time for each complete oscillation, called the period, is constant.What effects the time for one period?When the bob is moved from equilibrium either left or right and then is released, it oscillates in a vertical plane in the shape of an arc of a circle. This is then reversed back to its starting position.The weight pulling down on the pendulum bob causes the bob to accelerate towards its normal resting point. This acceleration can be calculated by the formula a = -gA. The angle size can also be linked to the arc length, this is shown in the formula, x = LA. With L being the length of the string. This leads us to the equation for acceleration of a simple pendulum bob a = -g/L x. These two formulae then give us the formula for a period, this isWhere L = length of string from pivot to bobg = acceleration due to gravityT = time of period.This tells me that there are only two variables, that I have direct control over, that can effect the period of the bob. These are the angle, and the length of the string. There is one other variable and that is the force of gravity; this could vary because the pull of gravity is not uniform all over the earth.PREDICTIONI predict that the longer the length of string the longer it will take the pendulum to complete one period. This is because the length of the arc, the pendulum is travelling along is greater (x = 2?L = circumference) but the gravitational acceleration will remain the same. This prediction is also proved by the formulaHere if the length of the string is increased (L) then that side of the equation becomes larger because the size of the fraction is increasing and because one side of the equation is increasing so must the other to remain equal so T will also increase.SAFETYThere are many accidents that could happen if this experiment was not carried out safely; below I have outlined a few simple guidelines to prevent such accidents occurring.DangerRiskPrecautionBob swingingCould hit someoneDo not swing the bob from large angles.Heavy massCould fall off table and hit someoneMake sure the mass isnt on the edge of the table and is away securely held.Clamp standCould fall over and hit someoneMake sure a large mass is holding it downFAIR TESTINGTo make sure our results are accurate we need to keep everything but the variable constant. Below are some simple guidelines to ensure that our testing is fair.Procedure/ObjectProblemSolutionClamp StandCould rockPlace a heavy mass on the base to prevent this.Mass of the bob (see note below)If we use different bobs there mass could be differentMake sure we use the same bobAngleAngle could be differentMake sure we measure the angle accuratelyGravityIf we move to another area of the world, the effects of gravity will be slightly differentStay in the same area of the earth as much as possible.Human errorHuman error between releasing the bob and starting the stopwatch.Make sure the same person does each task every time, use a standard pre-release method, i.e. 3,2,1, go. We should also let the pendulum swing for ten periods and then divide by 10 to reduce the effect of human error.Note: Although during my research I ascertained that the mass of the bob does not effect the period of the pendulum, I should still keep this constant, as I should only have one variable in my experiment.METHODAPPARATUSFor our experiment we needed:* A length of String at 60 cm long* A bob* A boss, clamp, and stand* A heavy mass* A large protractor* A Stopwatch* A meter ruler* A cork split in twoFirstly we set up the equipment as shown below:1. We measured the string to 10 cm. from the bottom of the corks to the middle of the mass.2. We t hen pulled the string back to 40?:3. We then released the bob and started the stopwatch at the same time.4. We let the bob swing backwards and forwards 10 times5. We then stopped the pendulum swinging and recorded the times.6. We repeated the experiment with the same length 3 times7. We then repeated steps 1-6 for string lengths 10cm, 15cm, 20cm 25cm, 30cm, 35cm, 40cm, 45cm, 50cm and 55cm.RESULTSLength of stringAttempt 1 (sec)Attempt 2 (sec)Attempt 3 (sec)Average for 10 oscillations (sec)Average for 1 oscillation (sec)107.067.317.207.190.719158.58.528.658.560.856209.769.599.679.670.9672510.8010.6210.8610.761.0763011.4811.4211.3911.431.1433512.4512.4812.3212.421.2424012.7212.8912.7712.791.2794513.9514.0313.8113.931.3935014.4214.6514.5614.541.4545515.8415.8515.4415.711.571ANALASISBy looking at my results, I can immediately tell that the longer the length of string the longer it takes the pendulum to complete one period. This increase in time is always between 30 second and 90 seconds. I have drawn a graph, which shows the period for each oscillation. My line of best fit shows that the time taken increases in a linear fashion and does not go through the point of origin. This shows me that the period does increase relative to the length of string, this supports my prediction that because of the length of the arc increasing with the length of the string that the period would increase.EVALUATIONI believe that my experiment went reasonably well, the results we collected would seem to be very good and we had no accidents. I also believe that the method we used to obtain these results was an accurate one, but it could have been improved with the use of light gates and a computer because this would have removed the element of human error. I would like to take this investigation further by continuing to increase the lengths of the string until about one-meter. I would also like to try this experiment with different angles to see what effect that has on the results and th en compare the results to these ones. The evidence I have here is only just enough to support a firm conclusion, but does show a trend appearing. A simple Pendulum Essay Example A simple Pendulum Essay My aim in this experiment was to see if the length of the string the bob was attached to effected the time taken for one oscillation.RESEARCHWhat a pendulum is:A pendulum is a body suspended by a fixed point so it can swing back and forth under the influence of gravity. Pendulums are frequently used in clocks because the interval of time for each complete oscillation, called the period, is constant.What effects the time for one period?When the bob is moved from equilibrium either left or right and then is released, it oscillates in a vertical plane in the shape of an arc of a circle. This is then reversed back to its starting position.The weight pulling down on the pendulum bob causes the bob to accelerate towards its normal resting point. This acceleration can be calculated by the formula a = -gA. The angle size can also be linked to the arc length, this is shown in the formula, x = LA. With L being the length of the string. This leads us to the equation for acceleration of a simple pendulum bob a = -g/L x. These two formulae then give us the formula for a period, this isWhere L = length of string from pivot to bobg = acceleration due to gravityT = time of period.This tells me that there are only two variables, that I have direct control over, that can effect the period of the bob. These are the angle, and the length of the string. There is one other variable and that is the force of gravity; this could vary because the pull of gravity is not uniform all over the earth.PREDICTIONI predict that the longer the length of string the longer it will take the pendulum to complete one period. This is because the length of the arc, the pendulum is travelling along is greater (x = 2?L = circumference) but the gravitational acceleration will remain the same. This prediction is also proved by the formulaHere if the length of the string is increased (L) then that side of the equation becomes larger because the size of the fraction is increasing and because one side of the equation is increasing so must the other to remain equal so T will also increase.SAFETYThere are many accidents that could happen if this experiment was not carried out safely; below I have outlined a few simple guidelines to prevent such accidents occurring.DangerRiskPrecautionBob swingingCould hit someoneDo not swing the bob from large angles.Heavy massCould fall off table and hit someoneMake sure the mass isnt on the edge of the table and is away securely held.Clamp standCould fall over and hit someoneMake sure a large mass is holding it downFAIR TESTINGTo make sure our results are accurate we need to keep everything but the variable constant. Below are some simple guidelines to ensure that our testing is fair.Procedure/ObjectProblemSolutionClamp StandCould rockPlace a heavy mass on the base to prevent this.Mass of the bob (see note below)If we use different bobs there mass could be differentMake sure we use the same bobAngleAngle could be differentMake sure we measure the angle accuratelyGravityIf we move to another area of the world, the effects of gravity will be slightly differentStay in the same area of the earth as much as possible.Human errorHuman error between releasing the bob and starting the stopwatch.Make sure the same person does each task every time, use a standard pre-release method, i.e. 3,2,1, go. We should also let the pendulum swing for ten periods and then divide by 10 to reduce the effect of human error.Note: Although during my research I ascertained that the mass of the bob does not effect the period of the pendulum, I should still keep this constant, as I should only have one variable in my experiment.METHODAPPARATUSFor our experiment we needed:* A length of String at 60 cm long* A bob* A boss, clamp, and stand* A heavy mass* A large protractor* A Stopwatch* A meter ruler* A cork split in twoFirstly we set up the equipment as shown below:1. We measured the string to 10 cm. from the bottom of the corks to the middle of the mass.2. We t hen pulled the string back to 40?:3. We then released the bob and started the stopwatch at the same time.4. We let the bob swing backwards and forwards 10 times5. We then stopped the pendulum swinging and recorded the times.6. We repeated the experiment with the same length 3 times7. We then repeated steps 1-6 for string lengths 10cm, 15cm, 20cm 25cm, 30cm, 35cm, 40cm, 45cm, 50cm and 55cm.RESULTSLength of stringAttempt 1 (sec)Attempt 2 (sec)Attempt 3 (sec)Average for 10 oscillations (sec)Average for 1 oscillation (sec)107.067.317.207.190.719158.58.528.658.560.856209.769.599.679.670.9672510.8010.6210.8610.761.0763011.4811.4211.3911.431.1433512.4512.4812.3212.421.2424012.7212.8912.7712.791.2794513.9514.0313.8113.931.3935014.4214.6514.5614.541.4545515.8415.8515.4415.711.571ANALASISBy looking at my results, I can immediately tell that the longer the length of string the longer it takes the pendulum to complete one period. This increase in time is always between 30 second and 90 seconds. I have drawn a graph, which shows the period for each oscillation. My line of best fit shows that the time taken increases in a linear fashion and does not go through the point of origin. This shows me that the period does increase relative to the length of string, this supports my prediction that because of the length of the arc increasing with the length of the string that the period would increase.EVALUATIONI believe that my experiment went reasonably well, the results we collected would seem to be very good and we had no accidents. I also believe that the method we used to obtain these results was an accurate one, but it could have been improved with the use of light gates and a computer because this would have removed the element of human error. I would like to take this investigation further by continuing to increase the lengths of the string until about one-meter. I would also like to try this experiment with different angles to see what effect that has on the results and th en compare the results to these ones. The evidence I have here is only just enough to support a firm conclusion, but does show a trend appearing.