Question

LAB 4 – PENDULUM

Objective: The overall objective of the lab is to investigate the period of oscillation of a pendulum which all depends on its mass, length, amplitude.

Table 1 Dependence of Period on Mass for a Fixed Length and Amplitude

Trial	Mass, m (kg)	Period, T (s)
1	0.20	2.46
2	0.40	2.46
3	0.60	2.46
4	0.80	2.46
5	1.00	2.46
6	1.50	2.46

Length = 1.5 m                       Amplitude = 15⁰

Table 2 Dependence of Period on Length for a Fixed Mass and Amplitude

Trial	Length, l (m)	Period, T (s)
1	0.50	1.42
2	1.00	2.01
3	1.50	2.46
4	2.00	2.84
5	2.50	3.18

Mass = 1.5 (kg)                     Amplitude =15⁰          

Table 3 Dependence of Period on Amplitude for a Fixed Length and Mass

Trial	Amplitude,  (deg)	Period, T (s)
1	2	2.00
2	4	2.00
3	6	2.00
4	8	2.00
5	10	2.00
6	12	2.00

Length = 1.00 m                     Mass = 0.80 kg

1.)What goes in the last columns of the three tables?

2.)Analysis: Is the period constant with less than 1-2% deviation from the average value for any of the variables in the above Tables? Support your response with calculations and draw conclusion.

3.)Is there a variable that shows strong correlation with period T? Is that relation linear (T α l)? How can you tell? Explain and justify your answer. [The symbol ‘α’ means ‘proportional to’]

4.)To check other possibilities like T α l^1/2 or T α l^1/3, first calculate (length)^1/2 and enter values in the first blank column – type in the column heading with unit (m^1/2). On a graph paper, plot T on the y-axis and l^1/2 on the x-axis. Does it produce a straight line? If yes, what is the proportionality?

5.)If not, calculate (length)^1/3 on the last column, plot T vs. l^1/3 as above in search of a linear relation.

Does this produce a straight line? If yes, what relation between T and l does this suggest?

Answer 1

Sol:

1. The time period goes in the last column.

2. Yes, the time period is constant for mass and it is also constant for amplitude. But not for length.

3. Yes, there is a strong correlation between time period T and length l. But it is not  

4. If we will add one more column in table-2 for squaroot of length i.e. and will calculate corresponding values then we will a strong correlation of the form of