In this problem you will be analyzing a system that consists of a mass and a spring. The mass is known to be 0.9kg. The spring constant is known to be 2.9N/m. It has an oscillating force that is 2.8cos(wt) Newtons. This can be represented by: 0.9x² + 2.9x = 2.8 cos (wt) What would be the positive angular frequency that would lead to resonance? W=_ Without the complementary solution included, What would be the resonance part of the solution ? y₂=_

A tank contains 180 gallons of water and 50 oz of salt. Water containing a salt concentration of (1+sin 1) oz/gal flows into the tank at a rate of 5 gal/min, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? Round the values to two decimal places. Oscillation about a level = i Amplitude of the oscillation oz. oz.

The height of a buoy on a lake is changing during a storm. The height's rate of change can be modeled by r(t) = 0.5 cos(0.2t) feet per second where t is measured in seconds. Is the buoy's height increasing or decreasing at time t = 10 seconds? Why?

Near the grounds of a building is a windmill h(t)=2 cos (30t)+6, where h(t) is the height of the blade above the ground and t is the time in seconds. If the rotation begins at the blade with the highest possible height, at what time(s) will the blade be exactly 7.8m above the ground within the second rotation?