A mass of 20g stretches a spring 5 cm. Suppose that the mass is also attached to a viscous damper with a damping constant of 400 dyn-s/cm. If the mass is pulled down an additional 2 cm and then released, find its position u at any time t. Sketch the graph of u versus t. Determine the quasi-frequency and the quasi-period. Determine the ratio of the quasi-period to the period of the corresponding undamped motion. What kind of damping is there in this system? Remark: dyn (dyne) unit of force in centimeter-gram/second second. One dyne equals 0.00001 Newton.

Let r(t) = (2 sin (t), +2, 3cos (t)) 2π 1. Find the unit tangent vector T(t) 2. Find T'(t) 3. Find the tangent line to the graph at the point (0, 2, 3) 4. Find the arclength of the graph from t = 1 to t = 4 5. Find the velocity at t = 2. 6. Describe the graph of r(t)

millimeters. The dimensions of the box are x = 50 cm, y = 20 cm and z=15 cm. Find the exact 9. The possible error involved in measuring each dinmension of a rectangular box is ±0.1 millimeters. The dimensions of the box are x = 50 cm v = 20 cm and z=15 cm. Find the ehe %3D %3D error at the extremes and approximate error using differential.

A mass that weighs 8 lb stretches a spring 48 in. The system is acted on by an external force of 8 sin(8t) lb. If the mass is pulled down 3 in. and then released, determine the position u(t) in ft of the mass at any time t in seconds. NOTE: Assume that the u-aris is directed downwards. u(t) Determine the first four times at which the velocity of the mass is zero. NOTE: Enter the eract answers and exclude t = 0 as trivial. The first four times the velocity is zero are t =