# The motion of a weight on a spring can be described by a modified cosine function. The weight…

The motion of a weight on a spring can be described by a modified cosine function. The weight suspended from a spring is at its equilibrium point when it is at rest. When pushed a certain distance above the equilibrium point, the weight oscillates above and below the equilibrium point. The time that it takes for the weight to oscillate from the highest point to the lowest point and back to the highest point is its period. The equation

models the vertical displacement v of the weight in relationship to the equilibrium point at any time t if it is initially pushed up 3.5 centimeters. In this equation, k is the elasticity of the spring and m is the mass of the weight.

a. Suppose k = 19.6 and m = 1.99. Find the vertical displacement after 0.9 second and after 1.7 seconds. b. When will the weight be at the equilibrium point for the first time?

c. How long will it take the weight to complete one period?