A body of mass 20 g acquires a velocity of 5 cm/s after one second of its starting from the mean position. If the time period of motion is 5 seconds, calculate the kinetic energy, potential energy and total energy of the body.

Explanation

Given, m = 20 g, T = 5 s
`omega = (2pi)/(T) = (2pi)/(5)` rad/s
At ` t = 1s, v = 5 cm//s`
Since, `v = A omegacosomegat`
`rArr 5 = A xx (2pi)/(5) cos (2pi)/(5) xx 1 = A xx (2pi)/(5) cos 72^(@)`
` = (A xx 2 xx 3.14)/(5) xx 0.309 = 0.388 A`
`rArr A = 50//0.388 = 13` cm
Now, total energy, `E = (1)/(2) mA^(2)omega^(2)`
` = (1)/(2) xx 20 xx 13^(2) xx ((2pi)/(5))^(2)`
` = (10 xx 169 xx 4 xx 9.86)/(25)`
` = 2,666` erg
Kinetic energy, `K = (1)/(2)mv^(2) = (1)/(2) xx 20 xx 5^(2) = 250` erg
`therefore` Potential energy P = E - K
` = 2,666 - 250`
` = 2,416` erg