2. An RLC circuit has an initial voltage across the capacitor and polarity as ma

Question

2. An RLC circuit has an initial voltage across the capacitor and polarity as marked on the circuit shown below. The switch is closed at t = 0 and a current i(t) is assumed to flow clockwise in the circuit. Determine which expression correctly represents the Laplace-transformed value of current, i(s).

Note that the coefficient of the highest power of s in the denominator may have to be made unity.

V2 = 11 V

C2 = 8F, IC = 4V

L1 = 8H

R2 = 8 ohms

       8 s^ 2 +8s+8
       0.875 s^ 2 +s+0.01563
       ?0.875 s^ 2 +s+0.01563
       0.875 s^ 2 +s+8

1. A continuous time system has an output, y, which is a function of time and is given by y =4t ^3 ? 8. It is sampled at     a    frequency of 2 Hz. Determine the expression that correctly represent the discrete signal obtained after sampling    and its   value for n = 4. (Points : 10)

Explanation / Answer

Ans1: to convert it in discrete form replace t with n/fs

y(t)=4t^3-8 sampling by 2Hz frequency to convert it discrete

y(n)=4(n/f)^3-8

we know that f=2Hz put the value in the above equation

y(n)=4(n/2)^3-8

y(n)=1/2 n^3-8 is the answer

to calculate value at n=4 put n=4 in the final equationy

y(4)=1/2(4)^3-8=24

y(n)=1/2 n^3-8 at n=4,24

so option 3rd is correct

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