Simple pendulum

- A clamp with stand
- A split cork
- A Cotton Thread (about 2 meters long)
- A bob
- Vernier calliper
- Stop /watch
- Metre scale.

- Find the vernier constant and zero error of the vernier calipers and record it.
- Determine the mean diameter of the simple pendulum bob using the vernier calipers.
- Find the mean radius of the bob and represent it using ‘r’.
- Attach a string to the bob. The length of the pendulum, l is adjusted by measuring a length of (l-r) from the top of the bob.
- Put ink marks M1,M2 and M3 on the thread at distance of 50cm,60cm and 70cm from the C.G of the bob .
- Pass the thread through the splited cork with the 50 cm mark at the bottom of the cork and tighten the two cork pieces between the clamp.
- Fix the clamp in a stand kept on the table such that the height that the bob is just 2 cm above the laboratory floor.
- Mark a point A on the floor just below the position of the bob at rest.
- The equilibrium position of the pendulum is indicated by drawing a vertical line with a chalk on the edge of the table, just behind the string.
- Find the least count and the zero error of the stop watch. Bring its hands to the zero position.
- Move bob using the hand at an angle not more than 45
^{0}and leave it. See that the bob returns over the line without spinning. - The stop watch is started when the pendulum crosses the equilibrium position to any one side.
- When it passes the equilibrium position in the same direction the next time it has completed one oscillation.
- Just when the 20th oscillation is complete, count 20 and at once stop the stop watch.
- Note the total time taken for twenty oscillations from the position of both the hands of the watch.
- As we need two observations for the same length, repeat steps 12 to 15 one more time.
- Repeat the experiment for lengths 60cm, 70cm, 80cm, 90 cm, 100cm, 110 cm, 120cm and 130cm.
- In each case is calculated. In all cases it is found that is a constant.
- The mean value of is calculated and then the acceleration due to gravity is calculated using the relation (2).

The experiment is preformed as explained above. A graph is drawn with l along X axis and T^{2} along Y axis. The graph is a straight line, as shown in the figure.

**To find the length of the second’s pendulum**

A second’s pendulum is one for which the period of oscillation is 2 seconds. From the graph the length l corresponding to T^{2}=4 s^{2} is determined. This gives the length of the second’s pendulum.

**To find the length of the pendulum whose period is 1.5 seconds**

The length l corresponding to T^{2} =1.5^{2}=2.25 is determined from the graph.

**To find the period (T) for a length 105cm**

T^{2} corresponding to l=105 cm is determined from the graph. The square root of this gives T, the period of the pendulum for a length 105 cm.

**From the graph**

= ------cm/s^{2}

- Select the environment to perform the experiment from the 'Select Environment' drop down list.
- Select the shape of the bob of the pendulum from the 'Select Shape' drop down list.
- Select the material of the bob from the 'Select Material' drop down list.
- Select the type of the wire to be used from the 'Select Wire' drop down list.
- Use the 'Change Length' slider to change the length of the pendulum.
- Use the 'Change Dimension' slider to change the dimension of the bob used.
- Now release the bob.
- Clicking on the 'Show Protractor' button helps us to ensure that the angle of swing does not exceeds 45
^{0}. - Now click on 'Play /Pause' button to start the stopwatch. We can alternatively click on the the 'Start' or 'Stop' button on the stopwatch.
- The time for twenty oscillations is noted.
- Now the real lab procedure from steps 12 to 18 can be followed to complete the observations for finding the acceleration due to gravity.
- Clicking on the 'Answer' button displays the acceleration due to gravity for the corresponding environment.

**To find the diameter of the bob**

1 M S D = 1mm

10 V S D =9 M S D

1 V S D=9/10 M S D=0.9 mm

Vernier Constant, V.C.= 1 M.S.D.-1 V.S.D. = (1-0.9) mm = 0.1 mm = 0.01cm.

**Zero error of vernier callipers(e)**

- e=..............cm
- e=..............cm
- e=..............cm

**Mean zero error**

e =.......cm

**Mean zero correction**

c = -e = ......cm

SL No | Main Scale Reading MSR(cm) |
Vernier scale Reading VSR(dvs) |
(VSRxL.C) (cm) |
Diameter of the bob,D=MSR+(VSRx L.C)+c(zero correction) (cm) |

Mean Diameter,D |

Mean Diameter of the Bob, D= ……………cm

Mean radius of the bob, r =D/2 = .........cm

Least count of stop watch =..........s

Zero error of stop watch =...........s

Zero correction of stop watch =...........s

Table for length () and time (T)

Sl No | (l-r)cm | Length of the pendulum l (cm) |
Time for 20 oscillations | Time Period |
T (s) |
|||

t1(s) | t2(s) | Mean t(s) |
||||||

Mean value of .=…………..ms^{-2}

The acceleration due to gravity,

g = …………m/s^{2}

Acceleration due to gravity from graph

Value or l = AB = -----cm

Value for T^{2 }= BC = -----------cm

AB / BC = ………..

Acceleration due to gravity,

g=---------m/s^{2}

- Acceleration due to gravity (g) at the place
- By calculation =………….ms
^{-2} - From the graph =………….ms
^{-2} - Mean g =………….ms
^{-2}

- By calculation =………….ms
- Length of the seconds pendulum =………….m
- Length of the pendulum whose period is 1.5 s=……..m
- Period of the pendulum of length 105 cm=…….s

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