36. In the given figure, spring constant is K, viscous friction coefficient is B, mass is M and the system output motions is x(t) corresponding to input force F (t).
    
    Which of the following parameters related to the above system?
    

    1. Time constant =	1
    	M

    
    

    2. Damping coefficient =	B
    	2 √KM

    
    

    3. Natural frequency of oscillation = √	K
    	M

    
    Select the correct answer using the codes given below :
    

1. 1. 1, 2 and 3

   
   
   

   2. 1 and 2

   
   
   

   3. 2 and 3

   
   
   

   4. 1 and 3

   
   
   

---

1. View Hint View Answer Discuss in Forum

   F(t) = M	d2x(t)	+ B	dx(t)	+ Kx(t)
   	dt2		dt

   
   The characteristic equation is,
   Ms² + Bs + K = 0
   or s ² + 2 ω_n s + ω_n ² = 0
   
   Thus statements 2 and 3 are correct.

   Correct Option: C

   F(t) = M	d2x(t)	+ B	dx(t)	+ Kx(t)
   	dt2		dt

   
   The characteristic equation is,
   Ms² + Bs + K = 0
   or s ² + 2 ω_n s + ω_n ² = 0
   
   Thus statements 2 and 3 are correct.

---

37. A system is represented by the block diagram given in the figure :
    
    Which of the following represents the input output relationship of the above diagram?
    

1. 1. 
      

   
   
   

   2. 
      

   
   
   

   3. 
      

   
   
   

   4. 

   
   
   

---

1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

---

---

38. The transfer function C/R of the system shown in the figure is
    

1. 1. 	G1 G2 H2
      	H1 (1 + G1 G2 H2)

   
   
   

   2. 	G1 H2
      	H1 (1 + G1 G2 H2)

   
   
   

   3. 	G2 H2
      	H1 (1 + G1 G2 H1)

   
   
   

   4. 	G2 H1
      	H2 (1 + G1 G2 H2)

   
   
   

---

1. View Hint View Answer Discuss in Forum

   It is a very simple block diagram and simply by inspection we see that
   

   	C(s)	=	1		H2G1
   	R(s)		H1		(1 + H2G1G2)

   Correct Option: B

   It is a very simple block diagram and simply by inspection we see that
   

   	C(s)	=	1		H2G1
   	R(s)		H1		(1 + H2G1G2)

---

39. The transfer function of a linear system is
    

1. 1. ratio of the output, v_o (t), and input v_i (t)

   
   
   

   2. ratio of the derivatives of the output and the input

   
   
   

   3. ratio of the Laplace transform of the output and that of the input with all initial conditions zeros

   
   
   

   4. none of these

   
   
   

---

1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

---

---

40. The closed loop system shown in the figure is subjected to a disturbance N(s). The transfer function
    

    	C(s)	is given by
    	N(s)

    
    

1. 1. 	G1 G2
      	1 + G1 G2 H

   
   
   

   2. 	G2
      	1 + G2 H

   
   
   

   3. 	G1
      	1 + G1 H

   
   
   

   4. 	G2
      	1 + G1 G2 H

   
   
   

---

1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

---