1. A 500-g block is placed on a level, frictionless surface and attached to an ideal spring. At t = 0 the block moves through th
e equilibrium position with speed vo in the –x direction, as shown below. At t = sec, the block reaches its maximum displacement of 40 cm to the left of equilibrium. a. Determine the value of each of the following quantities. Show all work. • period: • spring constant: b. Using x(t) = A cos(t + o) as the solution to the differential equation of motion: i. Determine the form of the function v(t) that represents the velocity of the block. ii. Evaluate all constant parameters (A, , and o) so as to completely describe both the position and velocity of the block as functions of time. c. Consider the following statement about the situation described above. "It takes the first seconds for the block to travel 40 cm, so the initial speed vo can be found by dividing 40 cm by seconds." Do you agree or disagree with this statement? If so, explain why you agree. If not, explain why you disagree and calculate the initial speed vo of the block.
