An 8.00 lb weight stretches a certain spring 0.500 ft. with this weight attached, the spring is pulled 3.00 inches longer than its equilibrium length and released. find the equation of the resulting motion, assuming no damping.

x(t) = 0.75 Cos8t

Explanation:

we know

F = m g

k x = m g

k =

k =

k = 512 lb/s²

now,

m = 8 lb    k = 512 lb/s²

x(t) = C₁Cos8t + C₂Sin8t

at t = 0  x = 0.5 ft + 3 inch = 0.75 ft

C₁ = 0.75 ft

x'(t) = -0.75×8Sin8t + 8C₂Cos8t

at t=0      x'(0) = 0

 8C₂ = 0

hence

x(t) = 0.75 Cos8t

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

option number c is the right answer.