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2 Free Vibration of Single Degree of Freedom System
Prob. 2.20
2.21 In a spring–mass system, the parameters associated with vibration are m, c,
k and x. What are the corresponding quantities for torsional vibration?
2.22 What is the effect of increase of stiffness in the natural frequency?
2.23 How is the concept of logarithmic decrement utilised?
2.24 What is the importance of critical damping?
2.25 A spring–mass has a natural frequency of 12 Hz. If the spring stiffness is
reduced by 1000 N/m, the frequency is altered by 50%. For the original
system, determine the mass and the spring stiffness.
2.26 A spring–mass system has maximum velocity 20 cm/s and time period 1 s.
If the initial displacement is 1 cm, determine (a) the amplitude, (b) the initial
velocity, (c) the maximum acceleration and (d) the phase angle.
2.27 Find the natural frequency of the system in the figure. The bar AB is massless
and rigid.
Prob. 2.27
2.28 For the system shown in the figure, the bar AB makes oscillations in the
horizontal plane about XY. Determine the angular frequency of the system.
2 Free Vibration of Single Degree of Freedom System
Prob. 2.20
2.21 In a spring–mass system, the parameters associated with vibration are m, c,
k and x. What are the corresponding quantities for torsional vibration?
2.22 What is the effect of increase of stiffness in the natural frequency?
2.23 How is the concept of logarithmic decrement utilised?
2.24 What is the importance of critical damping?
2.25 A spring–mass has a natural frequency of 12 Hz. If the spring stiffness is
reduced by 1000 N/m, the frequency is altered by 50%. For the original
system, determine the mass and the spring stiffness.
2.26 A spring–mass system has maximum velocity 20 cm/s and time period 1 s.
If the initial displacement is 1 cm, determine (a) the amplitude, (b) the initial
velocity, (c) the maximum acceleration and (d) the phase angle.
2.27 Find the natural frequency of the system in the figure. The bar AB is massless
and rigid.
Prob. 2.27
2.28 For the system shown in the figure, the bar AB makes oscillations in the
horizontal plane about XY. Determine the angular frequency of the system.