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Lab Report - obtain the frequency of the simple pendulum and to analyze the effect of change in amplitude, length and mass on the frequency.

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Introduction

Physics (SL) Experiment

Research Question

 To obtain the frequency of the simple pendulum and to analyze the effect of change in amplitude, length and mass on the frequency?

PHYSICS EXPERIMENT

Research Question: To obtain the frequency of the simple pendulum and to analyze the effect of change in amplitude, length and mass on the frequency?

Variables to be used:

Length of the string (L)

Acceleration due to gravity (g)

Time period of the pendulum (T)

Amplitude (A)

Mass of the pendulum (M)

Hypothesis:

According to length: The frequency of the simple pendulum is inversely proportional to the length of the string it means that as the length of the string increases the frequency decreases and vice-versa.

According to amplitude: When the amplitude of the simple pendulum changes there is no change in frequency.  

According to mass: When the mass of the simple pendulum changes there is no change in frequency.

Thing which affect the variables:

  • String should be light and inextensible.
  • Experiment should be executed at room temperature.
  • To reduce air resistance fans and cooler should be switched off.

APPARATUSREQUIRED:

S.NO

APPARATUS

QUANTITY

1.

Venier caliper

1

2.

Utility stand

1

3.

Clamp stand

1

4.

Test tube clamp

1

5.

String(200cm3)

1

6.

Stopwatch

1

7.

Meter stick

1

8.

Metallic bob

Theory:

Simple pendulum, consist of a metallic bob, suspended by inextensible string from a rigid support .At the mean position, when the bob is at rest there is only gravitational force (g) acting on the bob this kept it at rest. When the horizontal force is applied on the bob then it moves towards its extreme position .From the extreme position it moves back to its mean position and move further to the extreme position on the other side and again back to its main position, this motion of simple pendulum, that is starting from mean position and back to it is known as ONE CYCLE.

Amplitude: It is the distance between the two extreme positions.

Time period (T):Time taken by simple pendulum to complete one cycle

Frequency:It is the reciprocal of the time period (f = 1/ T)

Formula used:

                                          T = 2pi (L/g) ^1/2

Effect of Change in Length on the Frequency:

As we know that frequency is reciprocal of the time period, so formula for frequency is:                                                

                                                            f = 1/2pi (g/L) ^1/2

We can see that frequency is inversely proportional to the length of the string so if we increase the length of the string the frequency of oscillation decreases or if we decrease the length of the string the frequency of oscillation increases.

Precaution:

  • Perform the experiment under guidance of concerning faculty
  • For accurate and précised results take at least 3 reading
  • Try to keep the environmental condition as constant as possible.
...read more.

Middle

Radius of the Mass (bob) – cm

Varying length:

For this part of the experiment the amplitude was kept constant at 10cm and the mass of the bob was pegged at 87.32 gms.

Radius of the bob (cm)

Length of string

 Total Length (cm)

Radius +length of string

Time for 20 Oscillations (sec)

.76 ± .05

67.24 ± .01

68

33.10 ± .01

33.25 ± .01

.76 ± .05

77.24 ± .01

78

35.45 ± .01

35.63 ± .01

.76 ± .05

89.24 ± .01

90

38.07 ± .01

38.09 ± .01

.76 ± .05

95.24 ± .01

96

39.33 ± .01

39.43 ± .01

.76 ± .05

111.24 ± .01

112

42.48 ± .01

42.56 ± .01

.76 ± .05

122.24 ± .01

123

44.51 ± .01

44.65 ± .01

.76 ± .05

129.24 ± .01

130

45.88 ± .01

45.84 ± .01

Table 2- Data collection of length vs. time

  • Effect of Change in Amplitude –

Constant Mass (bob) - centimeters (cm)

Constant Length - grams (gm)

Radius of the Mass (bob) - cm

Length of the string - cm

Varying amplitude:

The mass of the bob was set to 87.32gms and the length of the string was kept constant at 120.00cms.

Amplitude (cm)

Time for 20 oscillations (sec)

5 ± .05

44.04 ± .01

44.25 ± .01

11 ± .05

44.15 ± .01

44.09 ± .01

23 ± .05

44.18 ± .01

44.19 ± .01

32 ± .05

44.25 ± .01

44.28 ± .01

             Table 3- Data collection of amplitude vs. Time

Units:

Length = cm

Mass = gm

Vernier caliper = cm

Uncertainties:

Meter scale = +/- 0.

...read more.

Conclusion

image01.png

Figure 2- Length vs. Time square

Varying Amplitude:

Amplitude (cm)

Time for 20 oscillations (sec)

Avg. Time for 20 oscillations

Time for one oscillation

5.0 ± .05

44.04 ± .01

44.25 ± .01

44.15 ± .02

2.208 ± .001

11 ± .05

44.15 ± .01

44.09 ± .01

44.12 ± .02

2.206 ± .001

23 ± .05

44.18 ± .01

44.19 ± .01

44.18 ± .02

2.209 ± .001

32 ± .05

44.25 ± .01

44.28 ± .01

44.26 ± .02

2.213 ± .001

Table 2- Data processing of amplitude vs. timeimage02.png

Figure 3- Amplitude vs. Time

Varying Mass:

Mass of bob (gm)

Time for 20 Oscillations (sec)

Avg. Time for 20 oscillations (sec)

Time for 1 oscillation (sec)

87.22 ± .01

41.32  ± .01

40.25 ± .01

40.24 ± .01

2.012 ± .01

64.45 ± .01

40.37 ± .01

40.43 ± .01

40.40 ± .01

2.020 ± .01

62.92 ± .01

40.44 ± .01

40.53 ± .01

40.48 ± .01

2.024 ± .01

54.28 ± .01

40.48 ± .01

40.73 ± .01

40.60 ± .01

2.0320± .01

22.45 ± .01

40.37 ± .01

40.42 ± .01

40.39 ± .01

2.019 ± .01

Table 3- Data processing of mass vs. time

image03.png

Conclusion:

Aspect 1:

From the above data and results we have concluded that there is an impact on the frequency of a simple pendulum if changes its length and there is no effect on the change of mass and amplitude. To be very précised there is a slight effect on a change on the mass or amplitude but it is quiet negligible that’s why we do not consider them.

Aspect 2:

Due to the presence of air there might be some error introduce in the experiment so take necessary precaution to minimize the error.

There is possibility that while taking different readings the length of thread might be measured incorrectly, so make a mark on the thread to avoid any error.

Aspect 3:

  • Instruments should have least amount of error.
  • Avoid the factors that affect the experiment.

...read more.

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