# Math Help - Pit and Pendulum problem

1. ## Pit and Pendulum problem

A simple pendulum consists of a lead bead hanging from a fixed point atthe end
of a string of length L(metres). When the bead is moved slightly to one side and
then released, it will swing to and fro. The time taken for the bead toperform a
complete oscillation (i.e. to return to its starting point) is known asthe period, T
(seconds).

A group of students perform an experiment, timing small oscillations ofsuch a
simple pendulum, and obtain the following data.

Length L (metres) 0.6 0.7 0.8 0.9 1.0
Period T (seconds) 1.55 1.68 1.79 1.90 2.01

(a) Thispart of the question asks you to find a relationship of the form T = aLbbetween L and T.
Enter the data into your spreadsheet, and use apower regression facilities to find the regression equation.

(i) Write down the values of a, b and r (the correlation coefficient) given bythe calculator or spreadsheet.
(ii) Write down the equation for T in terms of L,expressing the constants to
2 decimal places.
(iii) Imagine that you are in the group ofstudents collecting the data. Explain,
as if to a fellowstudent, two difficulties which you would anticipate
in collectingaccurate data.

2. ## Re: Pit and Pendulum problem

Originally Posted by Magical
A simple pendulum consists of a lead bead hanging from a fixed point atthe end
of a string of length L(metres). When the bead is moved slightly to one side and
then released, it will swing to and fro. The time taken for the bead toperform a
complete oscillation (i.e. to return to its starting point) is known asthe period, T
(seconds).

A group of students perform an experiment, timing small oscillations ofsuch a
simple pendulum, and obtain the following data.

Length L (metres) 0.6 0.7 0.8 0.9 1.0
Period T (seconds) 1.55 1.68 1.79 1.90 2.01

(a) Thispart of the question asks you to find a relationship of the form T = aLbbetween L and T.
Enter the data into your spreadsheet, and use apower regression facilities to find the regression equation.

(i) Write down the values of a, b and r (the correlation coefficient) given bythe calculator or spreadsheet.
(ii) Write down the equation for T in terms of L,expressing the constants to
2 decimal places.
(iii) Imagine that you are in the group ofstudents collecting the data. Explain,
as if to a fellowstudent, two difficulties which you would anticipate
in collectingaccurate data.

Seems a bit odd that you would model oscillation with an exponential function instead of trigonometric...

3. ## Re: Pit and Pendulum problem

how would u have modelled it?

4. ## Re: Pit and Pendulum problem

Well since I know that it's oscillating, I would have used a sine curve...

5. ## Re: Pit and Pendulum problem

how would u have used the sine curve