Question

450n 360n 710n 1400n 230n a block is placed in oscillation on a frictionless horizontal surface attached to a spring that is also attached to a wall. If, when stretched away from equilibrium by 15cm and released, it oscillates with a period of 0. 25s, and if the mass of the block is 15kg, what force was required to stretch the spring by the initial 15cm?.

Answer 1

m = 15, P = .25, x = .15

F = -K x for spring

ω = (K/m)^1/2

ω^2 = K / m

K = m ω^2 = m (2 π f)^2 = m 4 π^2 / P^2

K = 4 π^2 m / P^2

F = K x = x * 4 π^2 m / P^2

F = .15 * 4 * π^2 * 15 / .25^2

F = 1420 N