Performing the real lab:

 

• The compound bar pendulum AB is suspended by passing a knife edge through the first hole at the end A.  The pendulum is pulled aside through a small angle and released, whereupon it oscillates in a vertical plane with a small amplitude. The time for 10 oscillations is measured. From this the period T of oscillation of the pendulum is determined.

 

 

•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  
•  

 

 

 

 

 

 

 

• In a similar manner, periods of oscillation are determined by suspending the pendulum through the remaining holes on the same side of the centre of mass G of the bar. The bar is then inverted and periods of oscillation are determined by suspending the pendulum through all the holes on the opposite side of  G. The distances d of the top edges of different holes from the end A of the bar are measured for each hole.The position of the centre of mass of the bar is found by balancing the bar horizontally on a knife edge. The mass M of the pendulum is determined by weighing the bar with an accurate scale or balance. 

 

•  A graph is drawn with the distance d of the various holes from the end A along the X-axis and the period T of the pendulum at these holes along the Y-axis. The graph has two branches, which are symmetrical about G. To determine the length of the equivalent simple pendulum corresponding to any period, a straight line is drawn parallel to the X- axis from a given period T on the Y- axis, cutting the graph at four points A, B, C, D. The distances AC and BD, determined from the graph, are equal to the corresponding length l. The average length l = (AC+BD)/2 and  l/T² are calculated. In a similar way , l/T² is calculated for different periods by drawing lines parallel to the X-axis from the corresponding values of T along the Y- axis. l/T² should be constant over all periods T, so the average over all suspension points is taken. Finally, the acceleration due to gravity is calculated from the equation g= 4π²(l/T²).

 

• T_min is where the tangent EF to the two branches of the graph crosses the Y-axis. At T_min, the distance EF = l = 2k_G can be determined, which gives us k_G, the radius of gyration of the pendulum about its centre of mass, and one more value of g, from g= 4π²(2k_G/T_min²) .

 

• k_G can also be determined as follows. A line is drawn parallel to the Y -axis from the point G corresponding to the centre of mass on the X-axis, crossing the line ABCD at P. The distances AP = PD = AD/2 = h and BP = PC = BC/2 = h′ are obtained from the graph. The radius of gyration k_G about the centre of mass of the bar is then determined by equation (4). The average value of k_G over the different measured periods T is taken, and the moment of inertia of the bar about a perpendicular axis through its centre of mass is calculated using the equation I_G=Mk_G².

 

 

Performing the simulation:

 

• Suspend the pendulum in the first hole by choosing the length 5 cm on the length slider.

 

• Click on the lower end of the pendulum, drag it to one side through a small angle and release it. The pendulum will begin to oscillate from side to side.

 

• Repeat the process by suspending the pendulum from the remaining holes by choosing the corresponding lengths on the length slider.

 

• Draw a graph by plotting distance d along the X-axis and time period T along the Y-axis. (A spreadsheet like Excel can be very helpful here.)

 

• Calculate the average value of  l/T² for the various choices of T, and then calculate g as in step 2 above.

 

• Determine k_G and I_G as outlined in steps 3 and 4 above.

 

• Repeat the experiment in different gravitational environments by selecting an environment from the drop-down environment menu. If the pendulum has been oscillating, press the Stop button to activate the environment menu.

 

Observations:

 

      To draw graph :

 

 

 

     To find the value of 'g' : 

 

 

 

 

 

    To find the radius of gyration and the acceleration of gravity (step 3 above):

 

Radius of gyration about the centre of mass k_G = EF/2 = ..................

Acceleration of gravity, g= 4π²(2k_G/T_min²) = ......................

 

     To find the radius of gyration (step 4 above):

 

  

 

Results:

 

Average acceleration of gravity, g= 4π²(l/T²) = ..................  m/s²   

Average radius of gyration of the pendulum about its centre of mass, k_G =  ..................  m

Mass of the pendulum M =  ..................  Kg

Moment of inertia of the pendulum about its centre of mass, I_G=Mk_G² =  ..................  Kgm²