Question

The displacement from equilibrium of a mass oscillating on the end of a spring suspended from a ceiling is given below, where y is the displacement (in feet) and t is the time in seconds. Use a graphing utility to graph the displacement function on the interval [0, 10]. Find the value of t past which the displacement is less than 3 inches from equilibrium. (Round your answer to two decimal places.) y = 1.79e−0.22t cos(4.9t)

Answer 1

Using MS Excel, the function is graphed from t=0 seconds to t=10 seconds. The figure is shown below.

For the second question, the equation given is

$y = 1.79 e^{-0.22tcos(4.9t)}$

When y is 3 inches or 0.25 foot, t is

$0.25 = 1.79 e^{-0.22tcos(4.9t)}$

Simplify by taking ln for both sides:

$ln(e^{-0.22tcos(4.9t)})=ln \frac{y}{1.79}$

Solving for t,

t = 1.34 seconds