Simple harmonic emotion will always occur if the force acting on the oscillators is proportional to displacement from some equilibrium position and always directed back towards equilibrium.
Where g is the acceleration of free fall. An experiment in which the period of simple pendulum is measured can be used as determine the acceleration of free fall. This experiment is repeated for different lengths of pendulum and the gradient of a graph of against L is / g. This provides an alternative to dynamics experiment in which a time for a body to fall through measured distance is determined, and g can be calculated from the equation motion.
The period of oscillations can be expressed by the following relationship: where,
T= Period of oscillation in seconds
Constant
L= length
G= 9.8 m/s -2 (m/s 2)
I will try to change the given formula in such a way –that. I can use it for my experiment. There is no mass the formula, therefore the mass will not matter.
G= gravitational acceleration
L= length
This is the gradient
So is directly proportional now I will plot
T= time
L= length
G= Gravitational acceleration
I predict a straight a line because 4 and G are constant. An equation of a straight line Y=Mx+c
O= because pendulum does not oscillates where there is no length.
Equipment Apparatus
Metallic bob
Stopwatch
Clamp
String
Ruler (100cm)
Variables
- It was fair test by keeping the height from which the pendulum has drop to same
- The dependent variable was measured for the time taken
- There’s an error in the stopwatch when timing
- When the string gets shorter the speed of the pendulum gets faster to do 10 oscillations.
Method
- I will firstly set up a clamp stand with a piece of string50 cm long attached to it
- A mass of 50g will be attached securely to the other end of the string
- The mass will be held to one side at an angle of 45degrees (measured with a protractor) and then released.
- A stop watched will be used to take time for oscillation
- This will be repeated a number of times, each time shortening the length of string by 10cm
- The length of the pendulum will be plotted against the period on a graph. The final length of string and mass will be decided after my preliminary investigation.
Apparatus
- Meter ruler
- Protector
- Clamp stand
- G-clamp
- Stop clock
- String
- Mass
The following factors will be considered when providing a fair test
- The mass will be a constant of 50g throughout the experiment
- Angle of amplitude shall be a constant of 45 degrees. This will ensure that there is no variation of the forces acting on the pendulum.
- The value of gravitational field strength will inevitably remain constant, helping me to provide a fair test.
- The intervals between the string lengths will increase by 10cm each time, This will help me to identify a clear pattern in my results
- If any anomalous results are identified, readings will be repeated. This will ensure that all the are sufficiently accurate
The following Factors are considered when providing a safe test.
- Care will be taken not to let the bob come into contact with anything whilst swinging the pendulum, as the weight is relatively heavy.
- The clamp stand will be firmly secured to the bench with G-clamp so that the clamp stand, will not move, affecting the results.
- Excessively large swings will be avoided ( angle of amplitude will be 45 degrees results of preliminary investigation):
Length of string (cm) Period (seconds)
50 2.58
40 2.31
30 2.11
20 1.78
10 1.39
My preliminary investigation was successful. The results from my table back up my prediction that, as the length of the pendulum increases, the period increases.
I learned from my preliminary investigation that my processed method might not give me a sufficient accurate result. These results may be inaccurate due to the slight error of measurement in time, height or length. I will also measure the time taken for 10 oscillation rather than 1 and divide the result the by 10. These two changes will hopefully help me to identify and eliminate anomalies, should they occur. They should also add to the accuracy of my results.
Obtaining Evidence
I used the method proposed in plan, taking three other readings of each value and measuring the time for 10 oscillations rather than for 1. During the experiment, I observed that each oscillation for the same length of the string seemed to be equal. This showed that the pendulum did not slow down as the number of oscillation increased. I took the safety measures described in my original plan.
During the experiment I was careful to use accurate measurements in order to obtain sufficiently accurate results, for example:
-
The string was measured with a meter ruler , to nearest mm , to insure that each measurement had a difference of exactly 10cm
- The angle of amplitude will be measured with a protector to the nearest degree to ensure that the angle remains constant throughout the experiment.
- A stop clock will be used to measure the period accurately. The period was measured in second with the stop clock measuring to the degree of two decimal place in second. However I have rounded each time to the nearest second to give appropriate result.
- The mass was measured using five 10g masses, to ensure that the mass remain constant throughout the experiment.
Results:
This result was done the 1st time we did the experiment. This result shows that if you decreased the length of the string from the pendulum it will decreased the time period.
This result was done the second time when I did the experiment.
This result shows that if you decreased the length of the string from the pendulum it will decreased the time period.
This result came from the second time I did the experiment but this time I used this formula this is because I would know if I had done my experiment correctly and to see if I had any anomalous result.
Analysis
Using the results from my table, I drew the graph to show what had been obtained from the experiment. The graph clearly shows a smooth curve with a positive gradient. This indicates that as the length of the pendulum is increased.
Although my second graph does not show a perfect straight line through the origin, a line of best of fit can be drawn to show this. This backs up the theory in my scientific knowledge, that P is directly proportional to L, I.E. if the length of the string was doubled, the period will be doubled. My table of results drawn from my experiment was extremely similar to the results produced from my scientific formula, showing that my experiment was successful. My two Graphs showed resemblance to my predicted graphs. Indicating that my results were sufficiently accurate and therefore, my proposed method was reliable for this experiment.
My findings indicate that the time period varies directly with the length of the string when all factors remain constant
