The dynamic system below has the following parameters: m₁ = 20 kg, m₂ = 15 kg, m3 = 10 kg, k₁ = 100 N/m, k₂ = 50 N/m,k3 = 75 N/m, k4 = 100 N/m, ks = 25 N/m, b₁ = 5 Ns/m, b2 = 7 Ns/m and b3 = 1.5 Ns/m. Displacement input is a unit step. displacement input K₁ ww x₁ (t) m1 E x₂(t) K4 W E b₂ x3(t) m3 m2 ground 1. Derive the dynamic system's mathematical model 2. Determine the dynamics system's transfer functions 3. Determine a state space representation of the dynamic system 4. Plot the system's response, X₁ X2 and x3 on the same graph 5. Plot the system's velocity, xi xż and x3 on the same graph 6. Determine the dynamics system's characteristic equation 7. Determine the roots of the characteristic equation K5 w b3 E 8. What can you conclude about the system based on the roots determined earlier 9. With b2 being a design variable, select an appropriate b2 such that the dynamic system has an overall damping factor of = 0.4

y is the angle an absolute value?

Please do the last three questions (2, 3 and 4)! Thank you in advance!  A seesaw that weights 45lbs and its 5m long is balanced on the fulcrum in the center.  1- Two children are sitting on opposite sides of each other on the seesaw. One child weights 50lbs and is sitting 0.7m on the left end. Where should the other child sit in order to be balanced on the seesaw if they weigh 42lbs?  2- Now, a third child wants to sit on the seesaw and weighs 30lbs and is sitting 1.25m in front of them and is closer to the fulcrum on the right side. What are the CW and CCW moment of the seesaw now? What is the net moment and direction?  3- Then, a fourth child wants to play on the seesaw and is on the left side of the plank in order to bring the system to equilibrium. How much does the child weigh (Calculate the pounds of force needed in order for rebalance?)  4- Now the fourth child leaves the other three children sitting on the plank. If the three children are sitting in the same potions as they did…

Please answer from  iv onwards as you have already sent me the answer to the other please show working and correct answer

x=-2-5-6/2m