Consider a 30.6 kg crate being lifted upward by a cable. at time t = 0 s, the crate is located at y = +8.00 m and has an upward velocity of 4.00 m/s. there are two forces acting on the crate: • a 300 n downward gravitational force that the earth exerts on the crate. • a 147 n upward tension force that the cable exerts on the crate. what is the maximum height of the crate?

Suppose that a mass of 2 kg is attached a spring whose spring constant is 50. the system is damped such that b = 12 . the mass is set in motion with an initial velocity of -8 m/s at a position 0 meters from equilibrium. set up and solve a differential equation that models this motion. write your solution in the form a cos ( ω t − α ) where α is a positive number. use your solution to fill in the information below: what is the amplitude of the motion? what is the value of ω ? what is the phase shift?