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# How does the suspended mass affect the time period of an oscillation of a spring?

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Introduction

Physics Lab Report: 5

GOOD SHEPHERD INTERNATIONAL SCHOOL

PHYSICS LAB REPORT: 5

SPRING PENDULUM

Physics Lab Report

Experiment No- 5

Teacher’s Instruction:

To study how the difference in mass affects the Time Period of a spring pendulum.

Research Question:

How does the suspended mass affect the Time period of an oscillation of a spring?

Variables:

1. Independent Variable:
• Mass Suspended (m)
1. Dependent Variable:
• Time Period (T)
1. Control Variable:
• Number of Oscillations (n)
• Dimensions of the Spring

Apparatus:

• A Clamp Stand
• A G- Clamp
• A Spring
• Weights to be suspended
• A Digital Stop Watch
• A digital balance

Procedure:

• The clamp stand is set up and held steady to the table top using a G- Clamp.
• A spring is suspended to the Clamp Stand.
• The uncertainty in the digital balance and the stop watch is noted.
• A weight is measured using a digital balance and suspended to the spring. Time period for a fixed number of oscillations is noted.
• A number of three readings were taken for each mass suspended.
• The suspended masses were 269.4 g, 359.4 g, 449.2 g, 539.9 g and 585.3 g.

Figure 1: The Experimental Arrangement

Spring

Weights

Meter Rule

Clamp Stand

Data Collection:

• Following were the recordings of the Time Period of the various masses suspended from the spring pendulum:
...read more.

Middle

Time Period of 'n=20' Oscillations [s]

Time Period (t) [s]

1

449.2

20

19.78

0.989

2

449.2

20

19.81

0.9905

3

449.2

20

19.91

0.9955

AVERAGE:

0.99

1. 539.9 g
 Sl.No Mass suspended - m [g] No. of Oscillations (n) Time Period of 'n=20' Oscillations [s] Time Period (t) [s] 1 539.9 20 21.72 1.086 2 539.9 20 21.84 1.092 3 539.9 20 21.63 1.0815 AVERAGE: 1.09
1. 585.3 g
 Sl.No Mass suspended - m [g] No. of Oscillations (n) Time Period of 'n=20' Oscillations [s] Time Period (t) [s] 1 585.3 20 22.65 1.1325 2 585.3 20 22.59 1.1295 3 585.3 20 22.71 1.1355 AVERAGE: 1.13

Data Analysis :

• The uncertainties in the time period of pendulum was taken to be the least count of the stopwatch which happened to be ±0.01 s.
• The final Time Periods with their uncertainties were as follows:

Table 1: Uncertainties of Time Periods

 Mass - g Value of time period - s 269.4 0.65 ±0.01 s 359.4 0.84±0.01 s 449.2 0.99±0.01 s 539.9 1.09±0.01 s 585.3 1.13±0.
...read more.

Conclusion

T=0.0125×m0.711
• Thus, the relation between T and m was found to be:

T=0.0125×m0.711

• Now the equation was tested for its accuracy by substituting the masses and finding out the resulting time period and cross checking it with the experimentally obtained time period.
 Mass - g Experimental Time Period – s (Range) Equation formed Value of resulting T - s remarks 269.3 0.64-0.66 T=0.0125×269.30.711 0.66 Near range 359.4 0.83-0.85 T=0.0125×359.40.711 0.82 Near range 449.2 0.98-1.00 T=0.0125×449.20.711 0.96 Near range 539.9 1.09-1.10 T=0.0125×539.90.711 1.09 Within range 585.3 1.12-1.14 T=0.0125×585.30.711 1.16 Near range

Conclusion and Evaluation:

The graph found at last was a straight line. Most points passed clearly through the line of best fit. I derived a relation between T and m which found to be near accuracy and hence the experiment conducted was very much a success.

If got an opportunity to do the experiment again I would be more careful in taking down           the readings and make sure that the spring has not crossed its elastic limit. On the whole the experiment yielded a positive result.

Spring PendulumPage

...read more.

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