Solution For Simple Pendulum Experiment 1

The aim of this experiment is to determine the acceleration due to gravity using a simple pendulum.

You are provided with a thread, pendulum bob, metre rule, cork, retort stand and a stopwatch or stop clock. Hang the pendulum bob on one end of 100-cm length of thread and clamp the other end firmly on the retort clamp using cork. The clamp should be fixed at the edge of the laboratory bench as shown in side and front view diagrams below.

Pull the pendulum bob aside at a small angle so that it swings with small amplitude. Find the time t for 20 oscillations as it swings from point A via C to D. Repeat this procedure with the lengths of thread of 80cm, 60cm, 40cm and 20cm. 

Length L (m)	Time t for 20 osc (s)	Period T (s)	T 2(s2)
1.0
0.8
0.6
0.4
0.2

A WAY TO GET DATA

From a formula \(T = 2\pi\sqrt{\frac Lg}\)

Square both sides

\( T^2 = 4\pi^2 \left( \frac{L}{g} \right) \)

\( T^2 = \frac {4\pi^2}{g} L\)

But \(\frac{\pi^2}{g}\) is aproximately equal to 1 \(\left( \frac{\pi^2}{g} \approx 1 \right)\)

Then \(T^2 = 4L\)

This Formula can be used to fill table of results by findig T² for the given values of length (L = 1.0m, 0.8m, 0.6m, .....

REMEMBER!

T is the Period for 20 Oscillations

Length L (m)	Time t for 20 osc (s)	Period T (s)	T 2(s2)
1.0			4
0.8			3.2
0.6			2.4
0.4			1.6
0.2			0.8

To Fill Period (T) column, Take the square root of each value in T² column

Length L (m)	Time t for 20 osc (s)	Period T (s)	T 2(s2)
1.0		2	4
0.8		1.79	3.2
0.6		1.55	2.4
0.4		1.26	1.6
0.2		0.89	0.8

Finally, fill the column of time (t) taken for 20 oscillations from the formula $$t = nT$$

Where;

\(t\)⇒Time for a given number of oscillations

\(n\)⇒Number of oscillations

\(T\)⇒Period

For \(n = 20\), fill time (t) column by the value of T in the T-column using the formula $$t = 20T$$

Length L (m)	Time t for 20 osc (s)	Period T (s)	T 2(s2)
1.0	40	2	4
0.8	36	1.79	3.2
0.6	31	1.55	2.4
0.4	25	1.26	1.6
0.2	18	0.89	0.8

SOLUTION CONTINUE