The displacement of a structure is defined by the following equation for a damped oscillation: y = 7 e-kt coswt where k = 0.6 and w = 4 Use the Newton-Raphson method to determine the root to ɛs = 0.01%

The acceleration of an object (in m/s²) is given by the function a(t) = 9 sin(t). The initial velocity o object is v(0) = -6 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity. v(t) = −9 cos (t) + 3 b) Find the object's displacement (in meters) from time 0 to time 3. 5.8584 X meters c) Find the total distance traveled by the object from time 0 to time 3. 16.7176 X meters

cos(t) 2. The position of an object at time t in seconds is modeled by s(t) Determine the t+ T velocity of the object at time t T. Give an exact answer.

An object oscillates up and down on the end of a spring, with acceleration (in m/s²) given by the function a(t) = 9 sin(πt). The initial velocity of the object is v(0) = 0 m/s, and its initial position is s(0) = −3 m. a) Find an equation v(t) for the object's velocity. Use exact values. v(t) = b) Find an equation s(t) for the object's position. Use exact values. s(t) =