The total mechanical energy of an oscillator is evaluated using the relation

MATHEMATICS · Multi-part · GCSE · Mathematics · Number · Number

Problem

E=\tfrac{1}{2}m\omega^{2}A^{2}

, where

m

is the mass,

\omega

the angular frequency and

A

the amplitude. The measured quantities carry small uncertainties: the percentage errors in

m,\;\omega

and

A

are

1\%,\;2\%

and

3\%

, respectively. (a) Derive an expression for the percentage error in the calculated value of

E

in terms of the individual percentage errors in

m,\;\omega

and

A

. (b) Using your expression, compute the percentage error in

E

for the given data.