The mass of the load lifted by crane is 4000kg. The period of vertical oscillations of the load...

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The mass of the load lifted by crane is 4000kg. The period of vertical oscillations of the load suspended by crane‘s rope due to its elastic deformations is T=0,5s.What is the staticdeformation (elongation) of the ropexst?The mass of the rope should be neglected; the stiffness of the crane is significantly higher than the longitudinal (tensional) stiffness of the rope.2. Write the dynamic equation of the oscillating system.Find the damping ratio of the oscillating system when the viscous damping coefficient of the damper is c=20 N·s/m, stiffness of the spring is k=200N/mand size of the oscillating mass is m=2kg.What is the law of oscillations x(t) after the system is disturbed by initial displacement x0=0,01m ?3.Write the dynamic equation of the oscillating system and the equation describing its oscillations x(t). Calculate maximal values of the dynamic displacement(or amplitude of oscillations) and the force, acting the base (or its amplitude) , when the following is given:p0=4310 Pa; A=0,0516 m2;
	
Document Preview: 1. The mass of the load lifted by crane is 4000 kg. The period of vertical oscillations of the load suspended by crane‘s rope due to its elastic deformations is T = 0,5 s. What is the static deformation (elongation) of the rope xst ?The mass of the rope should be neglected; the stiffness of the crane is significantly higher than the longitudinal (tensional) stiffness of the rope.2. Write the dynamic equation of the oscillating system. Find the damping ratio of the oscillating system when the viscous damping coefficient of the damper is c = 20 N·s/m, stiffness of the spring is k = 200 N/m and size of the oscillating mass is m = 2 kg.What is the law of oscillations x(t) after the system is disturbed by initial displacement x0 = 0,01 m ?3. Write the dynamic equation of the oscillating system and the equation describing its oscillations x(t). Calculate maximal values of the dynamic displacement  (or amplitude of oscillations) and the force, acting the base (or its amplitude) , when the following is given:p0 = 4310 Pa;	A = 0,0516 m2; O = 30 rad/s;	m = 44,5 kg; k = 35000 N/m;   c = 1260 N·s/m. 	(note:   F = p?A)4. Write the dynamic equation of the oscillating system. Find maximal speed and acceleration of the falling bungee-jumper body, if the following is given:mass of the jumper is 75 kg, stiffness of the rope k=150 N/m, and he passes position of static equilibrium (x=0) with a 10 m/s speed. What should be the height on which the upper end of the rope is attached, if the length of free rope is 10 m?5. Theoretical task:  Principles and means of vibroisolation6. Types of Frequency Response Functions (FRF) (4 cases of 1 DOF systems forced vibrations)

David · Accepted Answer

1. The mass of the load lifted by crane is 4000 kg. The period of 
vertical oscillations of the load suspended by crane ‘s rope due to 
its elastic deformations is T = 0,5 s.  
What is the static deformation (elongation) of the rope xst? 
The mass of the rope should be neglected; the stiffness of the 
crane is significantly higher than the longitudinal (tensional) 
stiffness of the rope. 
Solution: 
Given:
Now: 
 ( )      (  ) 
Where, 
  √
 
 
 
  
 
    
Therefore: 
 ( )      (  ) 
The static elongation of the rope can be calculated by balanced force along the vertical plane:
   
    
(  ) 

2. Write the dynamic equation of the oscillating system.  
Find the damping ratio of the oscillating system when the viscous damping 
coefficient of the damper is c = 20 N·s/m, stiffness of the spring is 
k = 200 N/m and size of the oscillating mass is m = 2 kg. 
What is the law of oscillations x(t) after the system is disturbed by initial 
displacement x0 = 0,01 m?
Solution: 
    √    √           
 
 
 
Therefore, the damping ration can be calculated as: 
                
 
  
 
  
  
     (            ) 
                              √
 
 
 √
    
   

 
 
Displacement equation: 
     
           
Where, 
    √
3. Write the dynamic equation of the oscillating system and the equation 
describing its oscillations x(t). Calculate maximal values of the dynamic 
displacement x̂  (or amplitude of oscillations) and the force, acting the 
base (or its amplitude) 
ˆ
base
F
, when the following is given: 
p0 = 4310 Pa; A = 0,0516 m
2
;  
Ω = 30 rad/s; m = 44,5 kg;  
k = 35000 N/m; c = 1260 N·s/m.  (note:   F = pA) 
Solution: 
Dynamic equation (balancing the equation in vertical direction):

The mass of the load lifted by crane is 4000kg. The period of vertical oscillations of the load suspended by crane‘s rope due to its elastic deformations is T=0,5s. What is the staticdeformation...

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