Determine the Laplace transformation of the time domain function 50e-4t (1) s+4 (2) 50/(4s + 1)2 (3) 50/(4s+1) (4) 50/(s+4) 3. Find the inverse Laplace transformation (2-1) of 50/ (5s+1)2 (1) 2te-t/5 (2) 0.5te-t/5 (3) 50e-5t (4) 2te-5t 4. What is the Laplace transformation of the voltage derivative dv/dt if the initial voltage is 25 volts? (1) s-25 (2) sV (3) sV 25 (4) None of the above 5. What is the Laplace transformation of the integral of v(t), v(t) dt ? (1) V/s2 (2) s (3) sV (4) V/s 6. What is the inverse transformation (Y-1) of 10/[s(5s + 1)]? (1) e-t/5 (2) 10(1 e-t/5) (3) 5(1 e-t/10) (4) None of the above 7. A charged capacitor responds in accordance with the following equation: dv/dt + v/RC = 0 The capacitor has an initial charge og 10V. if R= 5k? and C = 0.22uF, what is the voltage solution in the frequency domain and in the time domain? (1) V = 10[1/(s + 909.1)], v(t) = 10e-t/1.1ms (2) V = 5[1/(s + 1000], v(t) = 5e-t/1ms (3) V = 20[(s+2000)], v(t) = 20(1-e-5t) (4) none of the above 8. A high pass filter network (series C, parallel R) has a circuit equation of C (dvO/dt dvi/dt) + vO/R = 0 determine the transfer function of the network in the frequency domain if the initial conditions are zero. (hint: solve for V/V..)o (1) s+1/RC (2) 1/(s+1/RC) (3) s/(s + 1/RC) (4) none of the above 9. What is the Laplace transformation of a step function which is zero volts for t<0 and 10 volts for t0? (1) 10/s (2) 1/s (3) a/s (4) none of the above 10. What is the Laplace transformation of 5sin(10t)? (1) 5/(s+10) (2) 50/(s2 + 100) (3) 50?x2 (4) none of the above
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