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### 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/T*^{2}^{ }are calculated. In a similar way , *l/T*^{2} is calculated for different periods by drawing lines parallel to the X-axis from the corresponding values of *T* along the** **Y- axis. *l/T*^{2} 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= 4π^{2}(l/T^{2}).

*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= 4π^{2}(2k_{G}/T_{min}^{2}) *.*

- 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_{G}^{2}.

### 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/T*^{2} 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= 4π^{2}(2k_{G}/T_{min}^{2}) = ......................

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

## Results:

Average acceleration of gravity, g= 4π^{2}(l/T^{2}) = .................. m/s^{2}

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_{G}^{2} = .................. Kgm^{2}