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Simple Pendulum
Posted Date:
15 Aug 2007
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Posted By: Jose Mathew
Member Level: Platinum Posted Date: 15 Aug 2007
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TOPIC : SIMPLE PENDULUM
(TO FIND THE HEIGHT OF ROOM)
AIM
• TO study the factors upon which the period of oscillation of a simple pendulum depends.
• To find the height of the room or the laboratory by the method of oscillation using a simple pendulum arranged.
MATERIALS REQUIRED
A simple pendulum, metre scale, stop clock, bobs of different masses, wooden blocks, a long string which has greater than the height of the laboratory.
INTRODUCTION
The period of a simple pendulum may depend on the length, amplitude, size, or mass of the bob etc:- Since the period of a simple pendulum depends on its length this knowledge can be effectively used to find height of the lab.
THEORY
When amplitude is small, the period of oscillation (T) of a simple pendulum is given by T= 2pvl/g where l is the length of the pendulum measured as the distance b/w the bottom of the cork to centre of the bob and g, the acceleration due to gravity.
We have the relation for period T= 2 pvl/g, i,e., T is directly proportional to vl or T2 is directly proportional to l or l/T2is constant at a place.If period (TH) can be found corresponding to a length which the height (H) of the lab and knowing l/T2value at the place,the height (H) can be calculated by the formula H= (l/T2) TH2.
The height (H) is also calculated from the formula.
TH = 2 p vH/g
I,e. H = (TH2 )/4 p2 g
EXPERIMENTAL PROCEDURE
The pendulum is suspended from a fixed point. The radius of the bob is determined using wooden blocks. The length of the pendulum ‘l’ is first adjusted to be 0.6 m.
A chalk mark is made on the edge of the table to indicate the rest or equilibrium position. The bob is drawn to one side by a small distance and released. When the pendulum just passes the chalk mark a stop watch is started counting it as zero. When the pendulum again cross the chalk mark in the same direction it is counted as one and so on .
At the end of 20 oscillations the stop clock is stopped and the time is noted this is repeated once again and the mean value for 20 oscillations is found out. This time (t) divided by 20 gives the period of oscillations. T (time for one oscillations)
To find the (l/T2) value
The pendulum is arranged on a retort stand placed on a table. The time for 10 oscillations is found for different known length(l).the time for one oscillation period (T) corresponding to each of these length is found by formula T= t/20 It is found once again. Mean (l/T2 ) is found as shown in the tabular column.
To find the period (TH) corresponding to the length (H) of the laboratory:-
The bob is suspended from the ceiling of the lab. A spare fan hook at the ceiling is sufficient to suspend the bob. The bob should not touch the floor. The time for 20 oscillations is found. The period (TH) is calculated. The length of the pendulum which is the height (H) of the lab is calculated using the formula,
H = mean (l/T2) TH2
To find (H) by the given formula:-
Since the period (TH) corresponds to the height of the laboratory and the value of ‘g’ is known,(H) can be calculated by the formula H= (TH2/4 p2) g.
The mean of the height obtained by tabulation and formula is found. The height (H) thus obtained can be corrected by adding the height of the bob from the floor to it.
To find the dependence of period on mass :-
Length of pendulum( l) = 1 m= 100 cm
Table -I.
OBSERVATION &CALCULATIONS:-
a) To find the dependences of period an length:-
Diameter of the bob, d= 2.8 cm.
Radius of the bob, r = d/2 = 1.4 cm.
Table -1
b)To find dependence of period on amplitude.
Length of pendulum (l) = 1 m = 100 cm.
Diameter of the bob (d) = 2 cm.
Radius of the bob ( r ) = d/2 = 1 cm.
I,e. (l-r ) = 99 cm.
Table -2
c)To find the dependence of period on mass :-
Length of pendulum( l) = 1 m= 100 cm
Table -3
d) To find the height of the room –
diameter of the bob= 2.8 cm
Radius of the bob= 1.4 cm
Table -4
To find H from tabulation:-
H= mean (l/t2) TH2 = 24.49 x 16.4 = 401.6 cm = 4.02m
To find H by the formula
H= (TH2/4p2)g = 0.42 x 9.8 = 4.12 m
To find height of the bob from the floor
L= distance b/w bottom of the bob to floor +r = 1+ 1.4 cm = 2.4 cm = 0.024m
Corrected height (H) = (H +h) = 4.02 + 0.024 = 4.044 m
CONCLUSION
- time period of a simple pendulum increase With increase in length.
- Time period of a simple pendulum is independent of the amplitude of oscillation
- Time period of a simple pendulum is independent of the mass or radius of the bob of the pendulum.
- The height of the laboratory by the method of oscillation of the simple pendulum = 4.044 m
REFERENCE:
-Thomas E.V , A manual of Practical Physics, Tess Publishers , Thiruvalla
-Mathur D.S , elements of Properties of Matter , S. Chand & Co.
-Arora C.L Mechanics and Properties of matter , S. Chand & Co
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