You are provided with a retort stand, clamp and boss, a pendulum bob, a piece of thread, and other necessary apparatus. Carry out the fo lowing experiment:
- Set up the apparatus as shown in the diagram above:
- measure and record the distance = 130cm from the centre of the bob to the point of suspension of the pendulum
- displace the pendulum through a small angle and release. Allow the pendulum to oscillate freely;
- determine the time t for 20 complete oscillations;
- also, determine the period T of the oscillations
- evaluate T\(^{2}\) and L = -30;
- repeat the procedure for four other values of l = 110, 90, 70, and 50 cm
- in each case, determine t and evaluate T,T\(^{2}\) and L. Tabulate your readings.
- plot of a graph of T\(^{2}\) on the vertical axis against L on the horizontal axis, starting both axes from the origin (0,0)
- determine the slope, s, of the graph. Also determine the intercept, C, of the graph on the T\(^{2}\) axis;
- evaluate: i. k\(_{1}\) = \(\frac{4\pi^{2}}{s_{1}}\),
ii. k\(_{2}\) = \(\frac{c}{8}\) [Take \(\pi\) = \(\frac{22}{7}\)] - state two precautions taken to ensure accurate results.
(b)i. What is meant by the period of oscillation of an oscillating body?
i. Explain the acceleration of free fall due to gravity.
Explanation
Table of value/ Observation
| S/N | L(cm) | t\(_{1}\)(sec) | T | T\(^{2}\) | L |
| 1 | 130 | 45.70 | 2.29 | 5.22 | 100 |
| 2 | 110 | 42.00 | 2.10 | 4.41 | 80 |
| 3 | 90 | 38.00 | 1.90 | 3.61 | 60 |
| 4 | 70 | 33.10 | 1.66 | 2.74 | 40 |
| 5 | 50 | 28.70 | 1.44 | 2.06 | 20 |
Slope (s) = \(\frac{\bigtriangleup {T}^{2}}{\bigtriangleup {L}} = \frac{5.2-2.0}{100-18}\)
S = \(\frac{3.2}{82}\)
= 0.039
Intercept (c) = 1.3
Evaluation
K\(_{1}\) = \(\frac{4 \pi ^{2}}{s}\) = \(\frac{4{(\frac{22}{7})^{2}}}{0.039}\)
= \(\frac{4 \times 9.878}{0.039} = (\frac{39.51}{0.039})\)g = 1013g
K\(_{2}\) = \(\frac{c}{s} = \frac{1.3}{0.039}\) = 33.33
Precautions:
- l avoided conical oscillations.
- l ensured firm suspension of pendulum (
- l ensured reading is repeated (shown on the table).
- I avoided draught.
- I corrected for zero error of metre rule/stop clock
- I avoided parallax errors in reading the metre rule/stop clock.
(b)i. The period of oscillation of a body is the time taken for the body to make one complete to and fro movement.
ii. When a body is falling under its weight (alone), the rate of increase of its velocity with time (as a result of the earth's gravitational pull) is the acceleration of free fall due to gravity.