Problem I For the following l't order dynamic system a-t-x =10 , x(0)=1

Problem I For the following l't order dynamic system a-t-x =10 , x(0)=1.2 (a) Find the value of the time constant T such that the system settling time 1 = 3sec with the 
allowed steady-state error e55 = 2.5% (b) Sketch the response of this system; on the graph indicate steady-state value, settling time, and specified steady-state error 
Problem 2 For the following 2nd order dynamic system + (5b -10)x = 10u(t),.x(0)=.i(0)-= 0 (a) Find the range of values °lb for which this system is stable (b) Find the range of values of b for which the total response of this system has decaying oscillations 
Modify the given dynamic system as follows: 2e+ hhY + 25x = 10it(i), x(0)= .740) = 0 (a) Find the steady-state response of this system (b) Find the range of values of b for which maximum overshoot to the given step response does not exceed 30%, rise time is no greater than 1 sec., and settling time (considering 2% error) is no greater than 1.5 sec.