A body weighing 20 g has a velcoity `8cms^(-1)` after one second of its starting from mean position. If the time period is 8 seconds, find the kinetic energy, potential energy and total energy.

Explanation

Here, `m=20g, T=8s, omega=(2pi)/(T)=(2pi)/(8)=(pi)/(4)rad//s`
When `t=1s, v=8cms^(-1)`
Now, `v=Aomega cos omega t`
`8=Axx(pi)/(4) cos ((pi)/(4)xx1)=A xx(pi)/(4)xx(1)/(sqrt(2))`
or `A=(32sqrt(2))/(pi)`
Total energy `=(1)/(2)momega^(2)A^(2)`
`=(1)/(2)xx20xx((pi)/(4))^(2)xx((32sqrt(2))/(pi))^(2)=1280 ergs`
Kinetic energy `=(1)/(2)mv^(2)=(1)/(2)xx20xx8^(2)=640erg`
`PE= ` Total energy `-` Kinetic energy
`=1280-640=640erg`