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, ...
Question 1 Report
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.
Answer Details
Test of Practical Knowledge: Simple Pendulum
The drawing paper is fixed to the vertical board. The line RP is drawn as the rest position of the string, with P marked at the centre of the bob at rest. When the bob is displaced to a new position P¹, the perpendicular distance d of P¹ from the line RP and the vertical height h of P¹ above P are measured as shown below.
For each of the five positions the readings are taken and \(d^{2}\) and \(G=\dfrac{d^{2}}{h}\) are evaluated.
Table of readings (RP = 20 cm)
| S/N | d / cm | d² / cm² | h / cm | G = d²/h / cm |
|---|---|---|---|---|
| P₁ | 3.30 | 10.89 | 3.00 | 3.63 |
| P₂ | 5.50 | 30.25 | 2.80 | 10.80 |
| P₃ | 7.60 | 57.76 | 2.60 | 22.22 |
| P₄ | 9.60 | 92.16 | 2.40 | 38.40 |
| P₅ | 10.50 | 110.25 | 2.20 | 50.11 |
Sample evaluations: \(G_{1}=\dfrac{10.89}{3.00}=3.63\,\text{cm}\), and \(G_{5}=\dfrac{110.25}{2.20}=50.11\,\text{cm}\).
Oscillations
With the board removed, the bob is set oscillating through a small amplitude. Time for 20 oscillations, \(t = 21.76\,\text{s}\), \(n = 20\).
\[T=\frac{t}{n}=\frac{21.76}{20}=1.088\,\text{s}\]Graph of G against h
G is plotted on the vertical axis against h on the horizontal axis, both axes starting from the origin.
The best-fit line cuts the horizontal (h) axis where \(G=0\). Reading from the graph, the intercept on the horizontal axis is
\[I \approx 3.0\,\text{cm}\]Evaluation of A
\[A=\frac{1}{19.7\,T^{2}}=\frac{1}{19.7\times(1.088)^{2}}=\frac{1}{19.7\times1.1837}=\frac{1}{23.32}\]\[A \approx 0.0429\,\text{s}^{-2}\]Precautions (any two)
- Parallax error was avoided by viewing the metre rule and stopwatch scales squarely (line of sight perpendicular to the scale).
- Conical (elliptical) oscillation was avoided by releasing the bob so that it swung in a single vertical plane through a small amplitude.
(b)(i) Period vs Frequency
| Period (T) | Frequency (f) |
|---|---|
| The time taken to complete one complete oscillation (one to-and-fro cycle). Its SI unit is the second (s). | The number of complete oscillations made in one second. Its SI unit is the hertz (Hz). |
They are reciprocals: \(f=\dfrac{1}{T}\).
(b)(ii) Oscillatory vs Rotational motion
| Oscillatory motion | Rotational motion |
|---|---|
| A body moves to and fro (back and forth) about a fixed mean position along a path, repeating the motion at regular intervals. Examples: a swinging pendulum, a vibrating string, a loaded test tube bobbing in water, a vibrating tuning fork. | A body turns (spins) about a fixed axis passing through or near the body, every particle moving in a circle about that axis. Examples: the blades of a fan in motion, the Earth spinning about its axis, a spinning wheel. |
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