**Time Response of First Order Systems Objective Questions**

**1. First order system is defined as :**

a) Number of poles at origin

b) Order of the differential equation

c) Total number of poles of equation

d) Total number of poles and order of equation

**Answer:** d

**Explanation:** First order system is defined by total number of poles and also which is same as the order of differential equation.

**2. A unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________**

a) 3/(1+600s)

b) 2/(1+500s)

c) 5/(1+220s)

d) 2/(1+600s)

**Answer:** d

**Explanation:** a(t)= k[1-e^{^}-t/T] K=2

0.632= 1-e^{^}-10/T

T=600 sec

G(s)=2/(1+600s).

**3. The transfer function of the system is G(s) =100/(s+1) (s+100). For a unit step input to the system the approximate settling time for 2% criterion is:**

a) 100 sec

b) 4 sec

c) 1 sec

d) 0.01 sec

**Answer:** b

**Explanation:** G(s) =100/(s+1) (s+100)

Taking the dominant pole consideration,

S=-100 pole is not taken.

G(s)= 100/s+1

Now it is first order system, ts=4T=4 sec.

**4. If a first order system and its time response to a unit step are as shown below, the gain K is :**

a) 0.25

b) 0.8

c) 1

d) 4

**Answer:** d

**Explanation:** Y(s)/R(s)=K/1+sT+K

By, use of partial fraction, K/T/s+(K+1/T)

Taking inverse Laplace transform on both the sides

Y(t)=K/K+1[1-e^{^}(K+1/T)t] K=4

**5. The unit impulse response of a system having transfer function K/(s+a) is shown below. The value of a is :**

a) t1

b) t2

c) 1/t1

d) 1/t2

**Answer:** d

**Explanation:** G(s) = K/s+a

C(s) =K/(s+a) Since R(s) =1

C(t) =Ke^{^}-at

T=1/a

C(t) =0.37K

T= t2=1/a.

**6. A system with transfer function 1/Ts+1, subjected to a step input takes to seconds to reach 50% of step height. The value of t is :**

a) 6.9s

b) 10s

c) 14.4s

d) 20s

**Answer:** c

**Explanation:** The response of a first order system is:

A(t)=a[1-e^-t/T] ½= 1-e^-10/t

T= 14.43 sec.

**7.A first order system and its response to a unit step input are shown in figure below. The system parameters are____________**

a) a=5 and k=12

b) a=10 and k=5

c) a=5 and k=10

d) a=8 and k=9

**Answer:** c

**Explanation:** time constant=0.2 sec.

1/a=0.2

a=5

final value=lim_{s→0} sC(s) =K/a

K/a=2

K=10.

**8. Assertion (A): It is observed that step function is first derivative of a ramp function and impulse function is first derivative of a step function.**

**Reason (R): From the derived time response expression it is concluded that the output time response also follows the same sequence as that of input functions.**

a) Both A and R are true and R is the correct explanation of A

b) Both A and R are true but R is not correct explanation of A

c) Both A is True but R is false

d) Both A is False but R is true

**Answer:** b

**Explanation:** If response due to one standard signal is known then response due to other signals can also be derived.

**9. Laplace transform of unit impulse signal is :**

a) A/s

b) A

c) 1

d) 1/s

**Answer:** c

**Explanation:** Laplace response of impulse signal is one which implies Laplace response is systems response.

**10. Time response during steady state the output velocity matches with the input velocity but lags behind the input by T.**

a) True

b) False

**Answer:** a

**Explanation:** In first order systems the time response during steady state the output velocity matches.