A body executes SHM of time period 8 s. if its mass be 0.1 kg, its velocity 1 sec after it passes through its mean position be `4ms^(-1)`, find its (i) kinetic energy (ii) potential energy and (iii) total energy.

Options

A. 0.8 J, 1.6 J and 0.8 J
B. 0.8 J, 0.85 J an 1.6 J
C. 0.4 J, 0.4 J and 0.8 J
D. 0.2 J, 0.2 J and 0.4 J

Answer

B

Explanation

Here m = 0.1 kg, T = 8 s
`therefore" "omega=(2pi)/(T)=(2pi)/(8)=(pi)/(4)rad^(-1)`
When `t = 1 sec, v = 4 ms^(-1)`
`because v = omega A. cos omega t`
`4 = (pi)/(4)A.cos((pi)/(4)xx1)=(pi)/(4).A.(1)/(sqrt(2))" "[because "cos"(pi)/(4)=(1)/(sqrt(2))]`
`therefore" "A=(16 sqrt(2))/(pi)m`
`therefore` Kinetic energy, `K=(1)/(2)mv^(2)=(1)/(2)xx0.1xx(4)^(2)=0.8 J`
`therefore` Total energy `E = (1)/(2)m omega^(2)A^(2)`
`because` Total energy, E = KE + PE
`therefore" "PE = E - KE = 1.6 - 0.8 = 0.8 J`