A certain mass is supported by a spring such that it is at rest 1m above the ground. The mass is pulled up 0.5 m and released at t= 0, creating a periodic up and down motion called simple harmonic motion. It takes 1.8 seconds for the mass to return to its original position each time. O Draw a graph to show the height of the mass above the ground as a function of time for the first 5.4 seconds. -4)+c for b) Write an equation as a cosine function in the form h = ascos your graph in part (a). c) Use your equation to determine all the time(s) in the first 5 seconds where the height of the mass above the ground is 0.5 m. Full algebraic solution.

A yo-yo oscillates up and down like a sine function y(t)=sin(t). a) What is the displacement over the time interval [0,6π]?   b) What is the total distance traveled by the yo-yo over the same time interval?   c) What is the minimum velocity of the yo-yo? Minimum speed?   d) At what part of the cycle is the yo-yo increasing in speed but decreasing in velocity?

Parts A-C

A mass of 0.12 kg is sliding on a frictionless horizontal surface when it comes to a horizontal spring with Hooke’s constant k = 90 N/m. The mass is moving at 15 m/s. How far does the spring compress? What is the acceleration of the mass when the spring is fully compressed? How much time elapses between when the mass first encounters the spring, and when the spring reaches full compression? a.) Set up and solve for maximum compression distance. b.) Set up and solve for acceleration at maximum compression. c.) Set up and solve for the time to maximum compression.