Q1. Verikn kas the Matrix exponemtial for A=⎣⎡​00−ω0​​000​w0​00​⎦⎤​ (In which wo is a real-valued parameter) is given b-

[answerhappygod]

1 (25.85 KiB) Viewed 29 times

2 (24.32 KiB) Viewed 29 times

3 (24.32 KiB) Viewed 29 times

4 (29.25 KiB) Viewed 29 times

5 (61.62 KiB) Viewed 29 times

Q1. Verikn kas the Matrix exponemtial for A=⎣⎡​00−ω0​​000​w0​00​⎦⎤​ (In which wo is a real-valued parameter) is given b-? eAt=⎣⎡​cos(ω0​t]0−sin(ωωt)​010​sin(ωt)0cos(ω⋅t)​⎦⎤​
∣∣​x1​(x)xh​(t)​∣∣​=∣∣​01​−i−4​∣∣​∣∣​m1​(k)x2​(z)​∣∣​+1∣31​)4​(t) x(x)=∣∣​−11​∣∣​ −y=∣0​2​)[x1​(t)x2​(t)​∣ (6) celcolcte tha sintiezeu tranifen finticture (b) Coccuete the impola cespiou (c) colcolisin the camplete motput eefpens y (t) for a wirt Hep i-jan ingalt Conpsictr of y(2)
∣∣​x1​(x)xh​(t)​∣∣​=∣∣​01​−i−4​∣∣​∣∣​m1​(k)x2​(z)​∣∣​+1∣31​)4​(t) x(x)=∣∣​−11​∣∣​ −y=∣0​2​)[x1​(t)x2​(t)​∣ (6) celcolcte tha sintiezeu tranifen finticture (b) Coccuete the impola cespiou (c) colcolisin the camplete motput eefpens y (t) for a wirt Hep i-jan ingalt Conpsictr of y(2)
Q5 A=[−23​32​−3​]B=[30​]C=[1−1]D=0​ Given an unkwonn inctial cun dition x0​=x(0), the response to a unt step inpros applied at t=0 is −)(t)=914​e−t−941​e−4t(t⩾0) Determine the nonzero initial conditun, x, that sutisfies thert ihe a boute output respoun
For the given state equation y(t)=[0​2​][x1​(t)x2​(t)​] a. Calculate the associated transfer function. b. Calculate the impulse response. c. Calculate the complete output response y(t) for a unit step input signal, presuming the given initial conditions. d Identify the zero-input response component of y(t) e. Identify the zero-state response component of y(t)