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**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 = aL*^{b}between 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.