Your drill press is out of balance. Drill bit lateral vibration time history is given by the following equation. y = e^-0 5 cos(4t) Write an accurate logic algorithm for Newton's method. Starting at time = 0.0 seconds, determine a time at which lateral vibration is zero using 4 iterations of Newton's method constructed in a table. Starting at time = 0.1 seconds, determine a time at which lateral vibration is zero using 4 iterations of Newton's method constructed in a table. Starting at time = 1.0 seconds, determine a time at which lateral vibration is zero using 4 iterations of Newton's method constructed in a table. Plot lateral vibration versus time from 0 to 2.5 seconds. Compare your three answers in relation to your plot. Why did Newton's method results in three different answers? Discuss