9 multiple chioce questions in applied science

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= 5kΩ 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 (dv_O/dt – dv_i/dt) + v_O/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