A linear harmonic oscillator of force constant `2 xx 106Nm^(-1)` and amplitude `0.01m` has a total mechanical energy `160 J`. Among the followinhg statement , which are correct?
i Maximum `PE`is `100J`
ii Maximum `KE`is `100J`
iii Maximum `PE` is `160J`
iv Maximum `PE` is zero

Options

A. Both (i) and (iv)
B. Both (ii) and (iii)
C. Both (i) and (ii)
D. Both (ii) and (iv)

Answer

B

Explanation

Total mechanical energy is `E_(T) = 160 J`
`:. U_(max) = 160 J`
At extreme position `KE` is zero , Work done by spring force extreme position to mean position is `W = (1)/(2) kA^(2)`
`:. K_(max) = W = (1)/(2) (2 xx 10^(6) )(0.01)^(2) = 100 J`
`:. U _(min) = 160-100 = 60J`