Question

An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is ? = ?(?) = −cos(3?)− √3 3 sin(3?), ? ≥ 0, where ? is measured in centimeters and ? in seconds. (Take the positive direction to be downward.) a. Find the velocity and acceleration at time t. b. Find the times at which the mass is heading downward at a velocity of 3 cm/s. c. What is the instantaneous velocity at the times when the mass passes the equilibrium position? d. When does the mass pass through the equilibrium position for the first time? e. Find the first time at which the mass passes through the equilibrium position heading upward? f. At what times is the mass 0.5 centimeters below the equilibrium position heading in the upward direction? g. Graph the position, velocity, and acceleration functions for 0 ≤ ? ≤ 4? 3. h. Find the total distance traveled by the mass during the first 4? 3 seconds. i. When is the mass speeding up when heading upward?

Answer 1

As per guidelines four subparts are solved.