A particle of mass m executes SHM with an amplitude A. If its mass is changed to `1/4`m, then what will be its (i) new frequency and (ii) total energy?

Explanation

(i) Frequency, `n=omega/(2pi)=1/(2pi)sqrt(k/m)`, where k = force constant.
Let n. be the changed frequency.
`therefore" "n/(n.)=sqrt((m.)/m)or,n.=nsqrt(m/(m.))=nsqrt(m/(1/4m))=2n`,
i.e., the frequency will be doubled.
(ii) Total energy, `E=1/2momega^(2)A^(2)=1/2kA^(2)`, i.e., the total energy remains the same.