21. Figure shows a single degree of freedom system. The system consists of a massless rigid bar OP hinged at O and a mass m at end P. The natural frequency of vibration of the system is
    

1. 1. fn =	1	√	k
      	2π		4m

   
   
   

   2. fn =	1	√	k
      	2π		2m

   
   
   

   3. fn =	1	√	k
      	2π		m

   
   
   

   4. fn =	1	√	2k
      	2π		m

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Force in the spring F = 2mg [from equilibrium] Deflection as mass at P,
   
   

   x1 =	x	× 2a = 2x = 2 ×	2mg	=	4mg
   	a		k		k

   
   

   wn = √	g	= √	g	= √	k
   	s		x1		4m

   
   

   fn =	1	ωn =	1	= √	k
   	2π		2π		4m

   Correct Option: A

   Force in the spring F = 2mg [from equilibrium] Deflection as mass at P,
   
   

   x1 =	x	× 2a = 2x = 2 ×	2mg	=	4mg
   	a		k		k

   
   

   wn = √	g	= √	g	= √	k
   	s		x1		4m

   
   

   fn =	1	ωn =	1	= √	k
   	2π		2π		4m

---

22. A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of √3k/m, the ratio of the amplitude of steady state response to the static deflection of the spring is______ .
    

1. 1. 2

   
   
   

   2. 0.5

   
   
   

   3. 1.05

   
   
   

   4. 0.5

   
   
   

---

1. View Hint View Answer Discuss in Forum

   MF = ±	1	= ±	1	= 0.5
   	1- (ω/ωn)²		1 - 3

   Correct Option: D

   MF = ±	1	= ±	1	= 0.5
   	1- (ω/ωn)²		1 - 3

---

---

23. A single degree of freedom mass-spring-viscous damper system with mass m, spring constant k and viscous damping coefficient q is critically damped. The correct relation among m, k, and q is

1. 1. q = √2km

   
   
   

   2. q = 2√km

   
   
   

   3. q = √2k/m

   
   
   

   4. q = 2√k/m

   
   
   

---

1. View Hint View Answer Discuss in Forum

   wn =	q
   	2m

   
   

   q = 2mwn = 2m √	k
   	m

   
   q = 2√km

   Correct Option: B

   wn =	q
   	2m

   
   

   q = 2mwn = 2m √	k
   	m

   
   q = 2√km

---