The total energy of a particle executing simple harmonic motion is `16J`. What will be total energy of particle if amplitude is halved and frequency is doubled?

Options

A. 1J
B. 64J
C. 16J
D. 256J

Answer

C

Explanation

Total energy `= (1)/(2) m xx omega^(2) xx A^(2)`
`= (1)/(2)m xx (2pi f)^(2) A^(2)`
`= 2pi^(2)mf^(2)A^(2)," "(E_(1))/(E_(2)) = ((f_(1))/(f_(2)))^(2)xx ((A_(1))/(A_(2)))^(2) = (1)/(1)`