Bifilar Suspension - the technique will be applied to find the mass moment of inertia of a regular cross-section steel beam about its centre of gravity.

DIAGRAM:

APPARATUS:

PEOCEDURE:

• Take a ruler of range 1cm – 100cm and fix it straight with the help of two clamp stands.
• Take another ruler of range 1cm – 50cm and hang it to the scale which was placed above with the help of inextensible strings.
• Select the mid- point for both the scales which was chosen to be 50 cm for the scale placed above and 25cm for the scale placed below.
• Before starting the experiment the length of the stsring used and the length between the sclae placed above must be measured and noted.
• Now, start the experiment with a measure of 12 cm distance between the strings on both scales.
• After arranging the apparatus set the scale placed below for oscillation.
• Give the amplitude alomost equal to 20 degrees.
• Start the stop watch.
• Measure the time taken for 10 oscillations.
• Note down the value and repeat the procedure for 16cm, 20cm, 24cm, 28cm, 32cm.

RISK MANAGEMENT:

• Care must be taken while scale is oscillating i.e. it should not move in other directions.
• The reaction time should be on par with the oscillations.
• The measure should be selected i.e. distance from the string should be selected only after experimentation of all the possible values.
• The values below 12 cm did not favour the experiment because the ruler’s oscillations were not possible.

OBSERVATION TABLE:

PROCESSED DATA ANALYSIS:

RANDOM ERROR: 

= (Δ k avg/ k avg) x 100 %

= (4.12/ 29.09) x 100 %        = 14.13 %

GRAPH: 1

Graph analysis:

• The graph plotted above is between effective distance (D) and time period (T)
• The line is not passing through origin (0,0) indicating the presence of systematic error in the investigation.
• The graph above has a reasonable RMSE value 0.04628 indicating a well-defined relationship between the effective distance (D) and time period (T).
• As the graph shows non- linear relation and in order to get a linear fit graph, so the data has been processed by calculating 1/T and then plotted 1/T vs. D.
• As y→1/T, x→D

As this graph shows a nonlinear graph, T2 was calculated and then plotted T2 vs. D

To further understand the relationship between the two.

GRAPH: 2

Graphical analysis:

• The best fit line does not pass from the point (0, 0) origin. Thus the inverse of Time period square (T) does not show direct proportionality to the effective Distance (D) of the string i.e. D α 1/Tsquare and the Y-Intercept is -05010 s.

• The graph shows a linear relationship between the effective distance (D) and the time period (T), as the straight line is nearly passing through origin.
• The best fit line is within the uncertainity bar as it touches all the data points.
• The graph suggests a reasonable correlation of about 96.50% indicating a well defined relationship between the effective distance (D) and the time period  (T)
• The line is not passing through origin (0,0) indicating the presence of systematic error in the investigation.
• The graph is having a meaningful systematic error as line touches at y-intercept of  -0.4065.
• As the RMSE value is 0.2145 which is close to 0,

Since the graph shows a straight line, to further investigate whether it is a linearly proportional graph ,a  zero-zero graph was plotted as showin in graph 3.

GRAPH: 3

Graphical analysis:

• The max-minima graph plotted include the origin point on the graph, which shows a linear relationship between the effective distance (L) and the 1/time period square (T).
• The uncertainity of the readings is greater towards the minimum value of the data points, were the graph deviates more for minimum values and less for maximum values.

Systematic error:

Maxima Slope = 0.1090 s/cm

Minima slope = 0.09129 s/cm

Systematic error =  X 100

= ( 0.1090 – 0.09129/2) / 0.09429X 100

= 9.566 %

CONCLUSION:

• From the experiment conducted it is found that it is true and that as the distance increases the time period decreases.
• The straight line of the linear graph shows that there is a linear relationship between the mass of  the distance and time period.
• The y-intercept shows the error that exists in the experiment. The y-intercept is -0.051010 cm which is very low.
• From the graph it is found that k = 2
• The best fit line shows the accuracy of the experiment as the line coincides with most of the points and passes through the all the error bars.

The true value of spring constant is

• The accuracy depends upon the random error and as the random error is less that is 14.13% the experiment is more accuarate.
• Maxima-Minima graph shows the accuracy of the readings taken and the slope of the lines.
• The analysis of uncertainties and errors has been done and it is found that the systematic error is less.
• The random error is 12.13% and the systematic error is 9.566%.

Evaluation:

• The distance is taken till 32cm till the oscillations were possible.
• The human parallax error also accounts the reading.
• The string was not perfectly inextensible.
• The zero error may also effect the experiment.