Find the final value of vo using the final value theorem

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Reference no: EM13286559

1)the equation M (d^2 X(t)/dt^2)+ D dx(t)/dt+ k x(t)=f(t)
a)Find X(s)/F(s).
b)show pole zero-plot
c)let f(t)=d(t). Find the initial value of x(t) using the initial value theorem. Find the final value of x(t) using the final value theorem.
d) Let f(t)=u(t). Find the initial value of x(t) using the initial value theorem. Find the final value of x(t) using the final value theorem.

2)Let f(t)= (t-1)[u(t-1)-u(t-2.5)] where t is in seconds. Suppose f(t) is sampled every second starting at t=0. Ts=1 sec.
a) Find F(z).
b) Find the Fourier transform of the sampled signal. Sketch the magnitude of F(jw) vs. w.

3) there is current source i(t) and a L,R and C all in parallel with each other, vo is the voltage across C.
a) Find V0(s)/I(s)
b) Show the pole zero-plot.
c) Let V(t)=d(t). Find the initial value of v0(t) using the initial value theorem. Find the final value of vo(t) using the final value theorem.
d) Let i(t)=u(t). Find the initial value of vo(t) using the initial value theorem. Find the final value of vo(t) using the final value theorem.

Reference no: EM13286559

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