A student was supplied with a stop watch, two metre rules and a simple pendulum suspended from a ceiling and was asked to measure the height of the ceiling indirectly. He set the pendulum swinging through a small angle and measured the period of oscillation for different lengths of the pendulum. Since he was unable to measure the length of the pendulum directly, he measured the height of the centre of the pendulum bob above the floor. He obtained the results tabulated below. Height of bob above floor (mm) Time for 50 oscillations (s) 400 155.3 600 148.8 800 142.2 1000 134.0 1200 127.4 1400 119.2 1600 110.5 The period T of the pendulum of length l is given by T = 2n (1) where g is the acceleration due to gravity. But l = H – h where H is the height of the ceiling and h is the height of the centre of the pendulum above the floor. Therefore (H – h) T = 2n Plot a suitable graph to find the height of the ceiling H from the two intercepts using linear regression to fit the best straight line through the data points. Assume that g = 9.8 ms-2 (g could be obtained from the slope of the graph). Having obtained your values for H, answer the following questions: (a) Which value of H do you consider to be the least accurate? Give reasons for your choice and explain how the accuracy could have been improved. (b) Why was the bob set swinging through a small angle?
A student was supplied with a stop watch, two metre rules and a simple pendulum suspended from a ceiling and was asked to measure the height of the ceiling indirectly. He set the pendulum swinging through a small angle and measured the period of oscillation for different lengths of the pendulum. Since he was unable to measure the length of the pendulum directly, he measured the height of the centre of the pendulum bob above the floor. He obtained the results tabulated below. Height of bob above floor (mm) Time for 50 oscillations (s) 400 155.3 600 148.8 800 142.2 1000 134.0 1200 127.4 1400 119.2 1600 110.5 The period T of the pendulum of length l is given by T = 2n (1) where g is the acceleration due to gravity. But l = H – h where H is the height of the ceiling and h is the height of the centre of the pendulum above the floor. Therefore (H – h) T = 2n Plot a suitable graph to find the height of the ceiling H from the two intercepts using linear regression to fit the best straight line through the data points. Assume that g = 9.8 ms-2 (g could be obtained from the slope of the graph). Having obtained your values for H, answer the following questions: (a) Which value of H do you consider to be the least accurate? Give reasons for your choice and explain how the accuracy could have been improved. (b) Why was the bob set swinging through a small angle?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A student was supplied with a stop watch, two metre rules and a simple
pendulum suspended from a ceiling and was asked to measure the height of
the ceiling indirectly. He set the pendulum swinging through a small angle
and measured the period of oscillation for different lengths of the pendulum.
Since he was unable to measure the length of the pendulum directly, he
measured the height of the centre of the pendulum bob above the floor. He
obtained the results tabulated below.
Height of bob above floor
(mm)
Time for 50 oscillations
(s)
400
155.3
600
148.8
800
142.2
1000
134.0
1200
127.4
1400
119.2
1600
110.5
The period T of the pendulum of length e is given by
T = 2n
(1)
where g is the acceleration due to gravity. But l = H – h where H is the
height of the ceiling and h is the height of the centre of the pendulum above
the floor. Therefore
(Н — Һ),2
T = 2n
(2)
Plot a suitable graph to find the height of the ceiling H from the two
intercepts using linear regression to fit the best straight line through the data
points. Assume that g = 9.8 ms-2 (g could be obtained from the slope of
the graph). Having obtained your values for H, answer the following
questions:
(a) Which value of H do you consider to be the least accurate? Give reasons
for your choice and explain how the accuracy could have been
improved.
(b) Why was the bob set swinging through a small angle?
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