The amplitude of a particle executing SHM is made three-fourth keeping its time period constant. Its total energy will be

Options

A. `(E)/(2)`
B. `(3)/(4)E`
C. `(9)/(16)E`
D. None of the above

Answer

C

Explanation

The kinetic energy of a particle executing SHM is
`E = (1)/(2) m omega^(2)a^(2)" "["where, a = amplitude of particle"]`
`therefore" "(E')/(E)=(a'^(2))/(a^(2))=(((3)/(4)a)^(2))/(a^(2))" "(because a' = (3)/(4)a)`
`therefore" "E' = (9)/(16)E`