You are provided with two retort stands, two-metre rules, pieces of thread, and other necessary apparatus. ( see illustration above)
i. Set up the apparatus as illustrated above ensuring the strings are permanently 10cm from either end of the rule.
ii. Measure and record the length L = 80 cm of the two strings.
iii. Hold both ends of the rule and displace the rule slightly, then release so that it oscillates about a vertical axis through its centre.
iv. Determine and record the time t for 10 complete oscillations.
v. Determine the period T of oscillations.
vi. Evaluate log T and L.
vii. Repeat the procedure for four other values of L= 70 cm, 60 cm, 50 cm, and 40 cm
viii. Tabulate your readings.
ix. Plot a graph with log T on the vertical axis and log L on the horizontal axis.
x. Determine the slope, s, and the intercept, c on the vertical axis.
xi. State two precautions taken to ensure accurate results.
(b)i. Define simple harmonic motion.
ii. Determine the value of L corresponding to t= 12 s from the graph in 1.
Explanation
| S/N | L/CM | t/s | T=t/o/S | LogT/S | LogL/cm |
| 1 | 80.0 | 17.90 | 1.79 | 0.252 | 1.903 |
| 2 | 70.0 | 17.30 | 1.73 | 0.238 | 1.845 |
| 3 | 60.0 | 15.34 | 1.53 | 0.185 | 1.775 |
| 4 | 50.0 | 13.90 | 1.39 | 0.145 | 1.698 |
| 5 | 40.0 | 13.06 | 1.31 | 0.155 | 1.602 |
Slope (s) = \(\frac{\bigtriangleup \text{logT}_{2}}{\bigtriangleup\text{logL}_{2}}\) - \(\frac{\bigtriangleup \text{logT}_{1}}{\bigtriangleup\text{logL}_{1}}\)
= \(\frac{0.15 - 0.05}{0.164 - 0.148}\)
= \(\frac{0.100}{0.016}\) = 6.25
PRECAUTIONS
1. avoided zero error in the reciding of the stop watch
2. avoided Parallax in reading the metre rule and the stop watch
3. ensured that the support of the bifilar pendulum is rigid
4. ensured smooth and regular oscillations in a horizontal plane.
b. i. Simple harmonic motion is defined as the motion of an object whose acceleration is proportional to the distance from a fixed point and is always directed towards that point
see graph above