DOI : 10.17577/IJERTCONV3IS23023
- Open Access
- Total Downloads : 7
- Authors : Bhuvnesh, Phurailatpam Hemantakumar
- Paper ID : IJERTCONV3IS23023
- Volume & Issue : NCETRASECT – 2015 (Volume 3 – Issue 23)
- Published (First Online): 24-04-2018
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Measurement of Time Period of A Simple Pendulum using an Electronic Circuit
Bhuvnesh, Phurailatpam Hemantakumar
Department of Physics, Hindu College, University of Delhi
Abstract:- This project was taken up in the hope of building an electronic circuit which enables us to measure the time period of a simple pendulum accurately, taking into account the parallax, human reflex and random errors.
Measuring the time period of a simple pendulum by counting the number of oscillations and noting down the time using a stop watch is one of the simplest experiments one can perform to find the value of g, i.e. acceleration due to gravity. This experiment has restricted accuracy due the above mentioned errors. But the problem can be overcome to certain extent by employing an electronic circuit which reads the pendulums
movement, as well as count the time interval between oscillations. In this project an attempt is made to detect the pendulum using a laser detector with which a circuit consisting of timers and counters is employed to measure the number of oscillations and time of the journey simultaneously. The required result is allowed to display using 7447 IC and SSD (seven segment display).
The concepts involved in designing this project is well familiar with and read by any college student pursuing Bsc. Physics Hons.
LASER DETECTOR
DESCRIPTION OF THE COMPONENTS
LDR (light depending resistor) is an electrical component which changes its resistance according to how much light intensity falls on it.
A laser from a source is allow to fall on it continuously which keep the resistance of the LDR low. As the oscillating pendulum cuts the laser, the resistance of LDR goes high. This change in the LDR resistance is read with a circuit using two transistor. The transistor on the right is used as a switch and the output is derived from its collector terminal.
555 TIMER (AS MONOSTABLE MULTIVIBRATOR AND ASTABLE MULTIVIBRATOR)
R 4 8
+Vcc
Monostable multivibrator:
It has a stable and a quasistable state. A pulse at the trigger switches the
7 3
555 TIMER
5
output to quasistable state and stay for predetermined length of time. Then it switches back to the stable state and wait for the next pulse.
It is used to get a digital output wave with sharp edges.
6
C 1
2
TRIGGER
O.01uF
+Vcc
Figure 1: Monostable Multivibrator
Astable multivibrator:
R1 4 8
7 3
Neither the digital state is stable. Therefore the output switches back and forth between the two unstable state and it is periodic, rectangular
R2 555 TIMER
5
6
O.01uF
waveform.
This is used for timing the journey of the oscillating pendulum.
2 1
C
Figure 2: Astable Multivibrator
+5
A a
b
c
c
B 7447 d
e
C f
g
D
ICs (74160 and 74373):
+5
-
Seven segment display (common anode):
-
Digital output from counter is received by 7447 IC and is
-
converted to numerical form needed by SSD. The SSD
-
display the numerical output corresponding to the digital
-
output given by the counter.
f
g
Figure 3: Seven Segment Display with 7447 IC
74160 is a decade counter which can make digital count from 0000 to 1001, and repeats itself after each cycle. Every count is triggered through the clock pin.
74373 is an IC with 20 pins. It is internally D-flip flops which can be control with the enable pin provided. It also acts as a buffer to derive SSD display.
LASER DETECTOR 555 TIMER
MONOSTABLE
555 TIMER ASTABLE
+Vcc
CARRY OUTPUT
DECADE COUNTER 74160
DECADE COUNTER 74160
DECADE COUNTER 74160
DECADE COUNTER 74160
CLOCK
CARRY CLOCK CARRY CLOCK CARRY
DECADE COUNTER 74160
DECADE COUNTER 74160
CLOCK
DECADE COUNTER 74160
CLOCK
DECADE COUNTER 74160
OUTPUT OUTPUT OUTPUT OUTPUT
74373 D-flip flop LATCH
74373 D-flip flop LATCH
7447 IC 7447 IC 7447 IC 7447 IC
SSD SSD SSD SSD
Figure 4: Schematic diagram of the circuit used
Figure 4: Schematic diagram of the circuit used
EXPERIMENT
The pendulum is allowed to oscillate between the laser source and the detector. When at rest the laser, the bob of the pendulum and the LDR are made collinear. As the pendulum oscillates it cuts the laser which makes the detector to send a pulse and trigger the 555 timer (monostable). The timer outputs time period is set to be higher than the time the detector is obstructed while crossing the laser and lower than the time it takes to return to the mean position, i.e. when the timer is triggered again. The timer is then connected to a decade counter (74160 IC), which increase its count as the laser is cut, i.e. for every half oscillation. The carry output of 74160 IC goes to each enable pin of 74373 ICs which later will help in latching the output of the series counters.
The 555 timer (astable) is made to oscillate with a known frequency, by adjusting the value of capacitor and resistor used (87.5878Hz, for this experiment). It is then interface with a series of decade counters. These counters start counting as soon as there is an output from the 555 timer (astable) and the process continues. But the experiment dictates the requirement of time interval in certain number of oscillations. In order to achieve this 74373 ICs are employed to latch the counters output.
Each 74373 IC is control through enable pin by the carry output from the counter connected to 555 timer
(monostable). This counter counts from 0000 to 1001 and then starts from 0000 with a high carry output. As long as it is high, it enables the 74373 ICs and the output of the series counters is made available to be displayed by SSDs. When the former counter changes 0000 to 1000, its carry output goes low, thus disenabling the 74373 ICs. As a consequence the output display in SSD is latch till 74373 ICs are enable again.
Numbers displayed on SSDs are noted after every five oscillations for a particular pendulum length. Such ten readings are taken for nine different pendulum lengths and graph is plotted for each set, between the SSDs readings and number of oscillation. A line is drawn that fits the data points and the slope of this line will give the number of count made by the astable 555 timer per oscillation. The required time period of the pendulum can be obtained by multiplying the value of the slope with the least count of the astable 555 timer.
Comparison between the experimental results and theoretical values are made by plotting a graph between time period (T) and length of the pendulum (l). Further comparison can be achieved by plotting graph between l and T2.
The formula T=2/ is used to find the value of g.
OBSERVATIONS
Least count of the astable 555 timer = 0.011417 s
Theoretical value of g= 981cm/s2 g =acceleration due to gravity T= 2/ l = (g/42)T2 l = length of the pendulum
T = time period of the pendulum
Following are the graphs and tables to find the time period of the given length:
-
Pendulum length= 100 cm
Graph 1 Table 1
NO. OF OSCILLATIONS
SSDs READINGS
9568
10
10357
15
11227
20
12095
25
12965
30
13839
35
14715
40
15588
45
16464
50
17339
NO. OF OSCILLATIONS
SSDs READINGS
5
9568
10
10357
15
11227
20
12095
25
12965
30
13839
35
14715
40
15588
45
16464
50
17339
Slope=173.608 Time period= 1.982 s g=1000.49 m/s2
-
Pendulum length= 90 cm
Graph 2
Table 2
NO. OF
SSDs
OSCILLATIONS
READINGS
5
3544
10
4375
15
5206
20
6040
25
6874
30
7706
35
8540
40
9375
45
10209
50
11045
Table 2
NO. OF
SSDs
OSCILLATIONS
READINGS
5
3544
10
4375
15
5206
20
6040
25
6874
30
7706
35
8540
40
9375
45
10209
50
11045
Slope= 166.696
Time period= 1.903 s
g=981.12
cm/s2
-
Pendulum length = 80 cm
Graph 3
Table 3
NO. OF
SSDs
OSCILLATIONS
READINGS
5
5840
10
6615
15
7390
20
8166
25
8943
30
9722
35
10503
40
11283
45
12065
50
12847
Slope=155.719
Time period= 1.778 g=999.04 cm/s2
-
Pendulum length= 70 cm
Graph 4 Table 4
Slope=
NO. OF
OSCILLATIONS SSDs READINGS
5 5941
10 6675
15 7410
20 8145
25 8882
30 9623
35 10296
40 11035
45 11771
50 12504
145.525
Time period= 1.661 s g=1001.65 cm/s2
-
Pendulum length= 60 cm
Graph 5 Table 5
NO. OF OSCILLATIONS
SSDs READINGS
5
1955
10
2623
15
3292
20
3961
25
4629
30
5298
35
5966
40
6635
45
7303
50
7971
NO. OF OSCILLATIONS
SSDs READINGS
5
1955
10
2623
15
3292
20
3961
25
4629
30
5298
35
5966
40
6635
45
7303
50
7971
-
Pendulum length= 50 cm
Graph 6 Table 6
NO. OF OSCILLATIONS
SSDs READINGS
5
4310
10
4943
15
5577
20
6211
25
6841
30
7468
35
8094
40
8720
45
9346
50
9971
NO. OF OSCILLATIONS
SSDs READINGS
5
4310
10
4943
15
5577
20
6211
25
6841
30
7468
35
8094
40
8720
45
9346
50
9971
Slope= 125.771
Time period=
1.436 s
Slope=133.701 Time period=1.526 s g=1017.18 cm/s2
g=957.24 cm/s2
7. Pendulum length= 40 cm
Graph 7
Table 7
NO. OF OSCILLATIONS
SSDs READINGS
5
5443
10
6003
15
6563
20
7123
25
7682
30
8242
35
8803
40
9311
45
9870
50
10431
Slope= 110.668
Time period= 1.263 s
g=989.94 cm/s2
8. Pendulum length= 30 cm
Graph 8
Table 8
Slope= 97.0436
Time period=
1.108 s
g=964.72
cm/s2
NO. OF
5
9364
10
9848
15
10334
20
10819
25
11305
30
11790
35
12275
40
12761
45
13245
50
13730
5
9364
10
9848
15
10334
20
10819
25
11305
30
11790
35
12275
40
12761
45
13245
50
13730
OSCILLATIONS SSDs READINGS
9. Pendulum length= 20 cm
Graph 9 Table 9
Slope=
NO. OF OSCILLATIONS
SSDs READINGS
5
5848
10
6242
15
6635
20
7028
25
7422
30
7815
35
8208
40
8602
45
8996
50
9390
Slope=
NO. OF OSCILLATIONS
SSDs READINGS
5
5848
10
6242
15
6635
20
7028
25
7422
30
7815
35
8208
40
8602
45
8996
50
9390
78.6958
Time period= 0.896 s
g=983.49 cm/s
COMPARISON BETWEEN THE EXPERIMENTAL RESULTS AND THEORETICAL VALUE
Table 10: Time period of the pendulum in a particular length
X-AXIS
Y-AXIS
l (cm)
T (s)
20
0.898
30
1.108
40
1.263
50
1.436
60
1.526
70
1.661
80
1.778
90
1.903
100
1.982
Graph 10: Time Period VS Pendulum Length
Table 11: Relation between (time period)2 and length of the pendulum
X-AXIS
Y-AXIS
T2 (s2)
l (cm)
0.8064
20
1.2277
30
1.5952
40
2.0621
50
2.3287
60
2.7589
70
3.1613
80
3.6214
90
3.9283
100
NCETRASECT-2015 Conference Proceedings
Graph 11: Pendulum Length VS (Time Period)2
RESULT
It can be seen from the graph that the experimental data and the experimental curve are fairly close enough to the theoretical curve which are drawn with the assumption that g is 981cm/s2.
PRECAUTIONS
-
Least count of the astable 555 timer should be found accurately using a CRO, or a multimeter.
-
The counting done by the decade counter which is connected to monostable 555 timer is monitored with caution using LEDs at its output terminals, so that is doesnt skip its count.
-
Light condition of the room should not change as it may interfere with the desire detector output.
CONCLUSION
This project provides a platform where students learned to integrate various topics studied in digital electronics and classical physics. It also give exposure to troubleshooting, datasheets, design parameters and experimentation.
Besides this project, the method involved can be made to use in various other fields, like measuring rpm of a wheel etc.
ACKNOWLEDGEMENT
Special thanks to Maam Adarsh Singh for supervising the project.
REFERENCES
-
Digital principles and applications By Donald P. Leach & Albert Paul Malvino, (Glencoe, 1995).
-
Microprocessor Architecture, Programming, and Applications with the 8085 By Ramesh S. Gaonkar, (Prentice Hall, 2002).
-
NCETRASECT-2015 Conference Proceedings