Procedure

Apparatus

Kater's pendulum, stopwatch, meter scale and knife edges.

Procedure for Simulation

Step 1: Set Up the Parameters

1. Select your desired Environment (e.g., Earth) from the drop-down menu.
2. Set the values for the Mass of Steel Cylinder and Mass of Wood Cylinder using the sliders or input boxes.
3. Adjust the positions for Knife Edge $K_1$, Knife Edge $K_2$, Steel Cylinder, and Wood Cylinder using their respective sliders.
4. Verify all values. (Note: If any parameter combination is invalid, a pop-up alert will appear when you try to interact with the pendulum).

Step 2: Oscillating the Pendulum (First Position — $K_1$)

1. Displace the Pendulum: Click and hold the mouse on the Wood Cylinder, drag it slightly to one side (to give it an initial angular displacement), and release the mouse button to start the oscillation.
2. Start the Stopwatch: As the pendulum passes its central vertical position, click START on the stopwatch.
3. Count Oscillations: Count 10 complete oscillations (one complete back-and-forth movement equals 1 oscillation).
4. Stop the Stopwatch: Click STOP on the stopwatch as soon as the 10th oscillation completes. Record this time as $t_1$.
5. Stop Pendulum Motion: Click the STOP button under the Variables/Controls panel to halt the pendulum.

Step 3: Oscillating the Inverted Pendulum (Second Position — $K_2$)

1. Click the INVERT button on the control panel to flip the pendulum upside down.
2. Displace the Pendulum: Click and drag the cylinder slightly to one side again and release to start the oscillations.
3. Time 10 Oscillations: Use the stopwatch to measure the time for 10 complete oscillations in this inverted state. Record this time as $t_2$.
4. Click STOP under the control panel to stop the motion.

Step 4: Take Distance Measurements & Calculate

1. Check the Show Measurements checkbox to view the calculated distances:

• $h_1$: Distance from Knife Edge $K_1$ to the Centre of Gravity (C.G.).
• $h_2$: Distance from Knife Edge $K_2$ to the Centre of Gravity (C.G.).

2. Calculate time periods:

• $T_1 = \frac{t_1}{10}$
• $T_2 = \frac{t_2}{10}$

3. Substitute $T_1, T_2, h_1,$ and $h_2$ into the formula to calculate $g$:

$$g = \frac{8\pi^2}{\frac{T_1^2 + T_2^2}{h_1 + h_2} + \frac{T_1^2 - T_2^2}{h_1 - h_2}}$$

Real Lab Procedure

• Shift the weight W₁ to one end of Kater’s pendulum and fix it.
• Fix the knife edge K₁ just below W₁.
• Place the knife edge K₂ at the opposite end and fix the wooden weight W₂ symmetrically to balance the setup.
• Position the small weight w near the center of the rod.
• Suspend the pendulum about knife edge K₁ and record the time t₁ for 10 oscillations using a stopwatch.
• Calculate the time period using the equation: T₁ = t₁ / 10.
• Invert the pendulum and suspend it about knife edge K₂.
• Record the time t₂ for 10 oscillations and compute T₂ = t₂ / 10.
• If T₂ is not equal to T₁, adjust the position of knife edge K₂ so that T₂ approximately equals T₁.
• Balance the pendulum on a sharp wedge and mark the position of its centre of gravity.
• Measure the distance of the knife edge K₁ as h₁ and that of K₂ as h₂ from the centre of gravity.

Observations and Calculations

To determine T₁ and T₂

Distance of K₁ from C.G, h₁ = ............... m

Distance of K₂ from C.G, h₂ = ............... m

$$g=\frac{8\pi^{2}}{\frac{T_{1}^{2}+T_{2}^{2}}{h_{1}+h_{2}}+\frac{T_{1}^{2}-T_{2}^{2}}{h_{1}-h_{2}}}$$

Acceleration due to gravity, g =...............ms^-2.

Result

The acceleration due to gravity at a given place is found to be =...............ms^-2.