(Solved): Please use Matlab Simulink to answer. Thanks 1) Use Simulink to design and simulate a model file ...

Please use Matlab Simulink to answer. Thanks

1) Use Simulink to design and simulate a model file that represents the system in (2). Verify your result by comparing impulse response of this system with what you obtained during part 3.e of the pre-lab activities. 2) Consider a system with the following input-output relationship \[ \frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y(t)=3 \frac{d x(t)}{d t}+x(t) \] Using integrators, differentiators, adders, subtractors and gain modules, design this system. Record the step response of this system and compare that with the analytical solution and comment on that. Consider a system whose input-output relationship is given by the following differential equation where \( x(t) \) and \( y(t) \) are, respectively, the input and the output of the system. Assume that the system is at initial rest, i.e., if \( x(t)=0 \) for \( t \leq t_{0} \), then \( y(t)=0 \) for \( t \leq t_{0} \). a) Use your knowledge on differential equations to obtain \( y(t) \) for \( t \geq 0 \) when \( x(t)= \) \( u(t) \). Plot the so-obtained \( y(t) \) for \( 0 \leq t \leq 10 \). b) You can use function Is im to obtain the output of an LTI system to any input. Simply use Isim( \( a, b, x, t) \) where \( b \) and a are two vectors containing, respectively, the coefficients of the left-hand side and right-hand side, of the differential equation which describes the relationship between the input and the output of the system. \( \mathrm{x} \) is a vector containing the values of the input signal on a time grid define by vector \( t \). Make yourself familiar with function Is im and then use this function to analytically obtain the step response of the system in (2). c) Compare the results you obtained in parts a and b. d) Make yourself familiar with function step and then use this function to obtain the step response of the system in (2). e) Make yourself familiar with function impulse and then use this function to obtain the impulse response of the system in (2).