QUESTION 4The amplitude of vibration of an undamped system is measured to be 1 mm. The phase shiftfrom t=0 is measured to be 2 rad and the natural frequency is found to be 5 rad/s.a) Calculate the initial conditions (x(0) and v(0)) that caused this vibration to occur.Assume the response is of the form x(t) = Asin(wnt + p).b) Sketch its position in relation with time.

Given data:The amplitude of the vibration is, .The phase shift is, .The time taken is, .The angular…

Answered: QUESTION 4 The amplitude of vibration…

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

See similar textbooks

Similar questions

A free vibration test is conducted on an empty water tank shown in Figure 1. A cable attached to the tank applies F=120kN force with an angle a=46° to the vertical and pull the tank horizontally by u.-9cm. The cable is suddenly cut and the response of the tank is recorded. At the end of 4 complete cycles, the time is 2s, and the amplitude is 5cm. b) Determine the natural period and damping ratio if the tank is filled by water, Wwater =350kN. Figure 1
Figure 1 shows the vibration response of a spring-mass system (Figure 2) under initial disturbance. The response was recorded using an accelerometer (g = 9.81 m/s?). a) Determine the natural frequency of the system in rad/s. b) Determine maximum velocity and displacement. c) If another spring with equivalent stiffness is attached to the system, calculate the period of oscillation. 0.1 0.05 -0.05 -0.1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time(s) Figure 1 k m Figure 2 (6)epnyduy
A single degree of freedom mass-spring-damper system is subject to vibration under the influence of a harmonic force. On my site, it is given as m=2 kg, k=800 N/m, c=64 Ns/m. The amplitude of the harmonic force is F0=256 N and its frequency is w= 20 rad/s. Answer the questions in options a, b, and c according to the given information. 1) Calculate the damping ratio of the system (ξ) a.1 b.0.7 c.0.9 d.0.8 2)Calculate the magnification factor (M) of the system. a.0.86 b.1.25 c.0.312 D.0.625 3-) Calculate the maximum vibration amplitude (X) (meters). a.0.2 b.0.1 c.0.4 D.0.3
Q1/ An instrument vibrate with a frequency of 1 Hz when there is no damping. When the damping is provided, the frequency of damped vibrations was observed to be 0.9 Hz. Find (1) the damping factor, and (2) logarithmic decrement.
PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = 6000 kN/m. d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v (0) m (2) {2} cm. = cm, v (0) Sec 00000 m k 00000 k x₂ (1) 5k 0000 Figure 3 00000 k x₂ (1) m 00000 k X3 (1)
Find the total response of a single degree of freedom system with m=10kg, c=20Ns/m, k=4000N/m, x0=0.01m, and x˙0=0 under the following conditions:a) An external force F(t)=F0=100N and ω=10rad/s.b) Free vibration with F(t)=0.Are the total response in the two cases the same? Include your comments.
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
The 8kg body is moved to the right of the equilibrium position and released from rest at time t = 0. The viscous damping coefficient is 23NS/m and the spring stiffness, K is 38N/m. Determine the damping factor (ratio) of the system. Note: Give your answer to 3 decimal places. Other Parameters: Logarithmic Decrement (8): Answer: 2ng 2T C 8 = In = In1 = 5 wnTd = 5wn X2 Xn+1 1-5 wa 2m k Damping Ratio (5): 5= 2vkm 2mn V(21)2+8 Frequency of damped vibration (wa): wa = 1-Wn Undamped Forced Vibration: Frequency Ratio (): r- Xp-x sin w t Next page Hous page Type here to search
PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = 6000 kN/m. d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v(0)= {1} cm cm, v (0) = m Sec 00000 m k 00000 k x₁ (1) Jour 5k 0000 m Figure 3 00000 m 00000 k k x₂(1) - X3 (1) ܠܠܠܠܠܠܠܝ
Find the amplitude, period, and hori- zontal shift of the function, and graph one complete period. y = sin x +
Find the natural frequency (w) and the period (T). Given this value of mass (m) = 0.5 kg and spring constant (K)=857.8 N/m O A w = 41.42 rad/s, T=0.162s B. w = 51.42 rad/s, T=0.152s O Cw = 41.42 rad/s, T=0.152s
A 20 kg object is attached to a spring with spring constant 260 kg/s. It is also attached to a dashpot with damping constant c = 280 N-sec/m. The object is pushed upwards from equilibrium with velocity 5 m/s. Find its displacement and time-varying amplitude for t > 0. y(t) The motion in this example is O overdamped O underdamped O critically damped Consider the same setup above, but now suppose the object is under the influence of an outside force given by F(t) = 18 cos(wt). What value for w will produce the maximum possible amplitude for the steady state component of the solution? What is the maximum possible amplitude?

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS