For following scenarios, derive the system response and use plot function in matlab to plot the response. a) x(0) = 1, (0) = -2, f(t)=0 b) x(0) = 0, x(o)=0, f(t)=1 c) x(o) = 1, 3(0)=-2, f(1) =1 d) x(o)=0, x(0)=0, (t) = sin(51) e) x(0)=1,x(0)=-2, f(t)=sin(51) 8) (4pts) does the response in (c) equals the sum of (a) and (b)? does the response in (e) equals the sum of (a) and (d)? why? part 4: 9) (6pts) use only integrators to build the system. attach the simulink model. 10) (4pts) derive the equivalent transfer function from ſto x for the model in 9). is it the same as the transfer function in 1)? 11) (10pts) run simulation for the five scenarios in 7). plot the responses. are they the same as in 7)? part 5: 12) (6pts) use state space model to build the system again. attach the simulink model. 13) (4pts) use matlab function "ss2tf" to find equivalent transfer function from ſto x. is it the same as the transfer function in 1)? 14) (10pts) run simulation for the five scenarios in 7). plot the responses. are they the same as in 7)?