A roller coaster is pulled up to the top of a hill 45 m high. The cart then moves over the crest at an average speed of 0.5 m/s before it plunges down to its lowest point, 5 m above the ground. From there, it climbs over a second hill only 15 m high. What is the cart’s speed as it goes over the top of the second hill?

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?