A body of mass `1 kg` suspended an ideal spring oscillates up and down. The amplitude of oscillation is `1` metre and the periodic time is `1.57` second. Determine.

Options

A. Maximum speed of body.
B. Maximum kinetic energy
C. Total energy
D. Force constant of the spring.

Answer

A, D

Explanation

(i) Maximum speed of oscillating body
`v_(max) = Aomega = A xx (2pi)/(T)`
Here `A = 1` metre, `T = 1.57 s`
`v_(max) = (2 xx 3.14 xx 1)/(1.57) = 4 m//s`
(ii) Maximum kinetic energy
`K_(max) = 1/2 mv_(max)^(2) = 1/2 xx 1 xx (4)^(2) = 8J`
(iii) Total energy of particle will be equal to maximum kinetic energy
(vi) Time period of mass suspended by spring
`T = 2pi sqrt((m)/(K))`
so force constant
`K = (4pi^(2)m)/(T^(2)) = (4 xx (3.14)^(2)xx 1)/(1.57)^(2) = 16 N//m`