For Exercises 81–-82, consider a 1-kg object oscillating at the end of a horizontal spring. The horizontal position x(f) of the object is given by x(1) sin (wt) + xpcos(wi) WWW -3-2-1 0 1 2 3 where v, is the initial velocity, x, is the initial position, and w is the number of back-and-forth cycles that the object makes per unit time t. 81. At time t = 0 sec, the object is moved 3 ft to the left of the equilibrium position and then given a velocity of 4 ft/sec to the right (vo = 4 ft/sec). Vo sin(wt) + xocos (wi) to represent the a. If the object completes 1 cycle in 1 sec (w = 1), write a model of the form x(t) horizontal motion of the spring. b. Use the reduction formula to write the function in part (a) in the form x(t) = ksin(t + a). Round a to 2 decimal places. c. What is the maximum displacement of the object from its equilibrium position? 82. At time t = 0 sec, the object is moved 2 ft to the right of the equilibrium position and then given a velocity of 3 ft/sec to the left (vo = -3 ft/sec). a. If the block completes 1 cycle in 1 sec (w = 1), write a model of the form x(t) = sin (wt) + xọcos (wt) to represent the horizontal motion of the spring. b. Use the reduction formula to write the function in part (a) in the form x(t) = ksin(t + a). Round a to 2 decimal places. c. What is the maximum displacement of the object from its equilibrium position? Round to 2 decimal places.

For Exercises 81–-82, consider a 1-kg object oscillating at the end of a horizontal spring. The horizontal position x(f) of the object is given by x(1) sin (wt) + xpcos(wi) WWW -3-2-1 0 1 2 3 where v, is the initial velocity, x, is the initial position, and w is the number of back-and-forth cycles that the object makes per unit time t. 81. At time t = 0 sec, the object is moved 3 ft to the left of the equilibrium position and then given a velocity of 4 ft/sec to the right (vo = 4 ft/sec). Vo sin(wt) + xocos (wi) to represent the a. If the object completes 1 cycle in 1 sec (w = 1), write a model of the form x(t) horizontal motion of the spring. b. Use the reduction formula to write the function in part (a) in the form x(t) = ksin(t + a). Round a to 2 decimal places. c. What is the maximum displacement of the object from its equilibrium position? 82. At time t = 0 sec, the object is moved 2 ft to the right of the equilibrium position and then given a velocity of 3 ft/sec to the left (vo = -3 ft/sec). a. If the block completes 1 cycle in 1 sec (w = 1), write a model of the form x(t) = sin (wt) + xọcos (wt) to represent the horizontal motion of the spring. b. Use the reduction formula to write the function in part (a) in the form x(t) = ksin(t + a). Round a to 2 decimal places. c. What is the maximum displacement of the object from its equilibrium position? Round to 2 decimal places.