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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

image00.jpg

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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