A two degree of freedomundamped system has naturalfrequencies 2 rad/s and 3 rad/sand corresponding mode shapes{{{ and . A damping ratioof 2% is assumed for bothmodes. The initial displacementis {mm and initial velocity is{mm/s. The displacement ofthe first degree of freedom inmm at time t=3 s is0.3141O 0.56860.15330.1543

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Answered: A two degree of freedom undamped system…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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(1) The bar of mass, m= 10kg and length L=lm is fixed at the left end as shown below. Find; (a) The equations of motion of the system, k=2000N/m, k= 1000 N-m/rad. (b) The natural frequencies of the system (c) The response of the system if initial displacements are 01(0) =5rad and 0 2(0) = -5rad k, k k 30 kg Figure 1: spring - mass system
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PROBLEM5: a)Find the natural frequencies and mode shapes of the system shown in Figure 5. b) Find the free-vibration response of the two-degree-of-freedom system shown in Figure 5 with the initial conditions x₁ (0) = 1cm, and x₂ (0) = x₁(0) = x₂(0) = 0. Good luck h 2h 2k 2k mmm 2m 0.5K k mm Figure 5 m Tu2 0.5K Tul k mm
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Question 5. For the mass-spring-dashpot system in Fig.4, where M = 2 kg, K = 8 N/m and f,= 3 N-s/m, (a) obtain the transfer function of X(s) / F(s). (b) Specify the form of the time response after finding the damping ratio and natural frequency. (c) What would be the maximum and steady state values of the displacement, xmax and cs or c(0), respectively, when a constant 10 Nm torque is applied? (d) Write the general expression of the time response x(t). x(1). Solution 5. (a) The equation of motion of the system and the transfer function between the displacement and the force applied is found as follows, Fig.4
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Question 3 (a) A system is critically damped. Derive an expression for the time at which the dispacement achieves a maximum or minimum. What is the time that maximum displacement amplitude occurs for the following: For an aircraft landing, the natural frequency can be taken as 2.5 rad/s, initial displacement is 0 mm and sink rate, i.e. initial velocity is -50mm/s. For the result, roughy sketch the response of the system for the initial conditions. (b) The seat of a helicopter with a pilot weighs 1000N and is found to have a static deflection of 10mm under self-weight. The vibration of the rotor is transmitted to the base of the seat as harmonic motion with a frequency of 4Hz and an amplitude of 0.2mm. What are the levels of vibration felt by the pilot including velocity and acceleration?
The natural frequency of a system is determined to be 15 Hz ignoring the effects of damping. Calculate the damped natural frequency of the system assuming a damping ratio of 0.7.
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A two degree of freedom damped system has natural frequencies 2 rad/s and 3 rad/s and corresponding mode shapes {21}{ 2 1 } and {1−1}{ 1 − 1 } . A damping ratio of 2% is assumed for both modes. The initial displacement is {10}{ 1 0 }mm and initial velocity is {21}{ 2 1 }mm/s. The displacement of the first degree of freedom in mm at time t=3 s is
What’s the correct answer for this please ?
Sketch frequency response of the system from part (a) in the form of Bode plot as accurately as you can.

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