You are provided with three retort stands, a pendulum bob, a drawing board, a stopwatch, and other necessary apparatus. Using the diagram above as a guide, carry out the following instructions.
- Fix the drawing paper on the drawing board and hold the board with two clamps such that it is vertical.
- Suspend the pendulum bob such that it hangs freely in front of the drawing paper.
- Draw a line RP representing the rest position of the pendulum string and mark the position P of the centre of the pendulum bob at rest.
- Displace the pendulum bob to one side in a plane parallel to the drawing board.
- Mark the new position P\(^{1}\) of the centre of the bob.
- Measure and record the perpendicular distance, d of P\(^{1}\) from the line RP
- Evaluate and record d\(^{2}\).
- Measure and record the vertical height h of P\(^{1}\) above P.
- Evaluate G =\(\frac{d^{2}}{h}\)
- Repeat the procedure for four other positions of P\(^{1}\).
- Tabulate your readings.
- Remove the drawing board so that the pendulum bo can swing freely.
- Set the pendulum bob oscillating through a small bob amplitude and determine the time, t for 20 oscillations.
- Determine and record the period, T.
- Plot a graph with G on the vertical axis and h on the horizontal axis, starting both axes from the origin (0,0).
- Determine the intercept I on the horizontal axis.
- Evaluate A = \(\frac{1}{19.7T^{2}}\)
- State two precautions taken to obtain accuratee results. (Attach your drawing paper to your answer booklet.)
(b)i. Distinguish between the period and frequency of oscillation of a simple pendulum.
ii. Differentiate between oscillatory and rotational motions.
Explanation
| S/N | d/cm | d\(^{2}\)cm\(^{2}\) | h/cm | G = d\(^{2}\)/n/cm |
| P\(_{1}\) | 3.30 | 10.89 | 3.00 | 39633 |
| P\(_{2}\) | 5.50 | 30.25 | 2.80 | 10.80 |
| P\(_{3}\) | 7.60 | 57.76 | 2.60 | 22.22 |
| P\(_{4}\) | 9.60 | 92.16 | 2.40 | 38.40 |
| P\(_{5}\) | 10.50 | 110.25 | 2.20 | 50.11 |
Length Rp = 20cm
time taken = 21.76 seconds
n = 20
T = \(\frac{t}{n} = \frac{21.76}{20}\) = 1.088 seconds.
A = \(\frac{T}{19.7T^{2}}\)
A = \(\frac{3}{19.7 \times 1.088^{2}}\)
A = \(\frac{3}{23.320}\)
A = 0.1286cm/s\(^{2}\)
Precautions;
- Parallax error avoided when reading the meter rule/stopwatch.
- Conical oscillation avoided.
- Draught avoided during oscillation.
- Zero error noted and corrected for on the stopwatch/rule
- Neat traces.
(b)
| Period | Frequency |
|
- It is the time taken to complete one oscillations/cycle (to and fro motion) |
- It is the number of complete oscillations in one second. |
| Oscillatory motion | Rotational motion |
|
It's when a body moves in a to and fro manner (in a plane) Examples: Swing in motion pendulum in motion, vibrating string, loaded test tube, the vibration of tuning fork. |
It's when a body turns about an axis, through the body. Examples: blades of a fan in motion, motion of the earth about its axis. |