Question

An object of mass m is attached to a vertically oriented spring. The object is pulled a short distance below its equilibrium position and released from rest. Set the origin of the coordinate system at the equilibrium position of the object and choose upward as the positive direction. Assume air resistance is so small that it can be ignored.

a. Beginning the instant the object is released, select the graph that best matches the position vs. time graph for the object.
b. Beginning the instant the object is released, select the graph that best matches the velocity vs. time graph for the object.
c. Beginning the instant the object is released, select the graph that best matches the acceleration vs. time graph for the object.

Answer 1

x = A cos w * t is a good choice where w = angular frequency

a. When the object is released the displacement is a maximum and proceeds towards zero in a quarter of a cycle.

b. When the object is released the velocity is zero and proceeds towards its maximum value in a quarter of a cycle v = -w A sin w t

c. When the object is released the acceleration is a maximum since the quantity F = -K x is a maximum and the acceleration goes to zero in 1/4 cycle.

a = -w^2 A cos w t