introduction of compound pendulum experiment

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Lab report 4 compound pendulum experiment

Electrical engneering (ee-101), national university of sciences and technology.

• EJ Egibert 1 year ago Pendulum compound practical

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Preview text, date: 19 dec 2021, national universuty of science &, l ab report -, applied physics, department: nice, group name: j, group members reg., saad mehmood abbasi, hammad mehmood, sikander hayat khan,  suleman khan, ahmad shahab, title: study of compound pendulum.

In this experiment we will determine the value of gravitational acceleration ‘g’ and radius of gyration for the compound pendulum rod containing holes.

A compound pendulum has an extended mass, like a swinging bar, and is free to oscillate about a horizontal axis. The extended mass is called a rigid body in the case of the compound pendulum. For the simple pendulum the mass is concentrated in its bob, however the mass of the compound pendulum is distributed throughout the body.

For this experiment consider a rigid body AB of mass ‘m’ free to vibrate about a horizontal axis through the center of suspension ‘S’. ‘G’ is the position of center of gravity of the body for which the distance from the center of suspension to center of gravity ‘SG’ equals ‘ l ’.

The body would be displaced through a small angle ‘’. The torque acting upon the body due to its weight ‘mg’ would be

τ = mg x l sinθ

For which sin=since the angle is very small for the vibration so,

The torque produces an angular acceleration ‘’ in the body. If ‘I’ is the moment of inertia of the body about ‘S’ then

Iα =− mg lθ

The negative sign tells us that the acts to oppose angle ‘’. Radius of

gyration is defined as the distance from the center of mass to the center of gravity. Let ‘k’ be the radius of gyration of the body and its moment of inertia about ‘G’ is mk 2 .Thus total moment of inertia of the body is

I = mk 2 + ml 2

In this experiment we must find out the value of “g” and for this we are using compound pendulum. We will find time period of compound pendulum ten times.

• First, we will measure length of rigid body (given metal rod).
• Then we will find center of gravity or mid-point of metal rod.
• As given metal rod has holes, from center of gravity we have ten holes at either side left and right which we term as “Side A” and “Side B”.
• We will arrange clamp stand to hold metal rod.
• We have knife edge. Using it we will fix it at Side A first at the hole closest to center of gravity.
• We will balance the knife edge at wedge of clamp stand.
• Then displace the compound pendulum setup slightly (approx. 50 − 60 ¿
• Now note the time for ten vibrations two times.
• Then take mean of those two vibrations.
• Then divide the mean calculated by 10 to get values.
• Repeat step 5-10 for all other holes.
• Now graph is drawn by taking distance at x-axis and time at y- axis.
• Calculating “g” using:

Calculations and Observations:

Distance from center of gravity (cm)

Time period of 10 vibration s (t1 s)

Time period of 10 vibration s (t2 s)

Mean time for 10 vibration s t= ( t 1 + t 2 2

Time for 1 vibration T= t 10

• 3 31 32 32 3.
• 8 20 21 21 2.
• 13 17 17 17 1.
• 18 15 16 16 1.
• 23 15 15 15 1.
• 28 15 15 15 1.
• 33 15 15 15 1.
• 38 15 16 16 1.
• 43 16 15 16 1. 10 .

48 16 16 16 1.

Distance from Center of Gravity (cm)

Time Period of 10 vibrations (t1 s)

Time Period of 10 vibrations (t2 s)

Mean time for 10 vibrations t= ( t 1 + t 2 2

• 2 42 43 42 4.
• 7 23 23 23 2.
• 12 18 18 18 1.

A' D ' + B' E' 2

L 2 = 55 + 61 2

####### g 2 =

4 π 2 L 2 T 22

put the values in the above equation the value of g is 10 ms-

Mean value of g:

g 1 + g 2 2

ERROR IN THE VALUE OF g:

Percentage error in g =.

####### | experimental value − theoritical value |

theoritical value ×

Percentage error =

####### |9−9|

Conclusion:

Overall, our experiment proved the value of g to be 9 ms^-2 with an error of 1%.

Using the above-mentioned procedure, we calculated our two values of g. This was done

in order to reduce the error in our readings by taking their average. This error was later

####### L2 = 58cm

####### g = 9 ms- 2

calculated and turned out to be about 1%. Upon discussion we have found that error is due to:

 Parallax error  Disturbance in work environment  Method of release of road

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Course : Electrical engneering (EE-101)

University : national university of sciences and technology.

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practical physics

Sunday, 26 june 2016, experiment 10: compound pendulum.

• Plot the data in a graph similar to Fig. 2. Draw any horizontal line SS’. From the corresponding period T as determined by the ordinate of this line, and the length l of the corresponding equivalent simple pendulum as given by the average of the values of SO and S’O', calculate the acceleration g due to gravity, by means of Eq. (1) . Compare with the accepted value and record the percentage difference.
• From the mass m of the pendulum and the radius of gyration ko as determined from the graph, compute the rotational inertia Io about the axis G by Eq. (9). Compute the rotational inertia I about the axis S by Eq. (10).
• What is the minimum period with which this pendulum can vibrate? What is the length of a simple pendulum having the same period?
• Describe how Fig. 2 would be altered if the cylindrical mass M were near one end, say the end B.
• With a given, axis of suspension, say S, discuss the effect upon the period of (a) increasing the mass of the cylindrical body; (b) moving it nearer to S.
• How would the value of the minimum period To be affected by moving the mass M in either direction from the middle?
• With the mass M near the end B and the pendulum suspended about an axis S near A, how could the vibration of the system about the axis S’ be experimentally observed?
• Does the center of oscillation of a solid body, such as a rod or bar, lie within the body for any transverse axis of suspension? Explain.
• Locate the center of oscillation of a meter stick suspended about a transverse axis at the 10cm mark. At what other positions could the meter stick be suspended and have the same period?
• Prove that the period of a thin ring hanging on a peg is the same as that of a simple pendulum whose length is to the diameter of the ring.