TEST OF PRACTICAL KNOWLEDGE QUESTION You are provided with three retort stands, a pendulum bob, a drawing board, a stopwatch, and other necessary apparatus....

TEST OF PRACTICAL KNOWLEDGE QUESTION

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.

1. Fix the drawing paper on the drawing board and hold the board with two clamps such that it is vertical.
2. Suspend the pendulum bob such that it hangs freely in front of the drawing paper.
3. 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.
4. Displace the pendulum bob to one side in a plane parallel to the drawing board.
5. Mark the new position P\(^{1}\) of the centre of the bob.
6. Measure and record the perpendicular distance, d of P\(^{1}\) from the line RP
7. Evaluate and record d\(^{2}\).
8. Measure and record the vertical height h of P\(^{1}\) above P.
9. Evaluate G =\(\frac{d^{2}}{h}\)
10. Repeat the procedure for four other positions of P\(^{1}\).
11. Tabulate your readings.
12. Remove the drawing board so that the pendulum bo can swing freely.
13. Set the pendulum bob oscillating through a small bob amplitude and determine the time, t for 20 oscillations.
14. Determine and record the period, T.
15. Plot a graph with G on the vertical axis and h on the horizontal axis, starting both axes from the origin (0,0).
16. Determine the intercept I on the horizontal axis.
17. Evaluate A = \(\frac{1}{19.7T^{2}}\)
18. 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.

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)

1. Parallax error was avoided by viewing the metre rule and stopwatch scales squarely (line of sight perpendicular to the scale).
2. Conical (elliptical) oscillation was avoided by releasing the bob so that it swung in a single vertical plane through a small amplitude.

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(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.

Read lesson note on Motion (JAMB)

Read lesson note on Measurements And Units (JAMB)