NEED PARTS I-M PLEASEA large water tower holds 3 million gallons of water, which has a mass of about 11 million kilograms.When the wind blows, this causes the steel structure to sway back and forth due to the force. Anengineer studying the tower observes that a steady wind at a speed of 35 mph exerts a force of 1.45million Newtons on the tower, causing it to lean 0.27 meters away from equilibrium. The engineerbegins by assuming that the restoring force is proportional to the displacement F = -kx, so thatthe motion of the system can be modeled by the differential equation mx" + kx = 0. Here m is themass of the tower, k is the spring constant, and x is the displacement of the tower away from itsequilibrium position.(a) What is the spring constant k of the steel structure? Be sure to use the right units!(b) Write the general solution to the differential equation.(c) What is the angular frequency w at which the tower oscillates?(d) Suppose that the tower is sitting comfortably in equilibrium when a sudden brief gust of windgives the toof the tower changes after this?a velocity of 0.24 meters per second. What function will describe how the position(e) Make a plot of the position function from (d).(f) What is the maximum displacement away from equilibrium that the water tower goes? You canuse your graph as an aid, but use your function from (d) to get the exact value.(g) What is the period of the oscillation? That is, how much time does it take the tower to gothrough one complete cycle?(h) How would your plot be different if there had been a stronger gust of wind? What would be thesame? What would be different?(i) One month later, the tower is holding 21.5 million kilograms of water, when it experiences a gustof wind that again gives it a speed of 0.24 m/s. What function will describe the displacement ofthe tower?(j) Make a plot of the position function from (i).(k) What is the period of the new oscillation? You can use your graph as an aid, but use yourfunction from to get the exact value.(1) The steel framework will experience a catastrophic structural failure if it sways more than 1.2meters. What is the maximum speed that a gust of wind can give the tower while it's holding21.5 million kg of water before this causes unpleasant results.(m) Another engineer studies a similar tower in the neighboring town, finding that while this containson 9.5 million kilograms of water, it tends to sway back and forth with an angular frequency ofapproximately 0.55 rad/s. What must be the spring constant of the structure holding up thiswater tower?

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A large water tower holds 3 million gallons of water, which has a mass of about 11 million kilograms. When the wind blows, this causes the steel structure to sway back and forth due to the force. An engineer studying the tower observes that a steady wind at a speed of 35 mph exerts a force of 1.45 million Newtons on the tower, causing it to lean 0.27 meters away from equilibrium. The engineer begins by assuming that the restoring force is proportional to the displacement F = -kx, so that the motion of the system can be modeled by the differential equation mx" + kx = 0. Here m is the mass of the tower, k is the spring constant, and r is the displacement of the tower away from its equilibrium position. (a) What is the spring constant k of the steel structure? Be sure to use the right units! (b) Write the general solution to the differential equation. (c) What is the angular frequency w at which the tower oscillates? (d) Suppose that the tower is sitting comfortably in equilibrium when a sudden brief gust of wind gives the tower a velocity of 0.24 meters per second. What function will describe how the position of the tower changes after this? (e) a plot position function from (d). (f) What is the maximum displacement away from equilibrium that the water tower goes? You car use your graph as an aid, but use your function from (d) to get the exact value. (g) What is the period of the oscillation? That is, how much time does it take the tower to ge through one complete cycle? (h) How would your plot be different if there had been a stronger gust of wind? What would be the same? What would be different? (i) One month later, the tower is holding 21.5 million kilograms of water, when it experiences a gus of wind that again gives it a speed of 0.24 m/s. What function will describe the displacement o the tower? (j) Make a plot of the position function from (i). (k) What is the period of the new oscillation? You can use your graph as an aid, but use you function from to get the exact value. (1) The steel framework will experience a catastrophic structural failure if it sways more than 1.3 meters. What is the maximum speed that a gust of wind can give the tower while it's holding 21.5 million kg of water before this causes unpleasant results.