1. A thin disk attached to the end of an elastic beam has three uncoupled modes of vibration. The longitudinal motion, transverse motion and the torsional oscillations are all kinematically independent. Calculate the following for the system shown. a. Longitudinal stiffness b. Transverse stiffness c. Torsional stiffness 65 cm I r=10 mm E-200 x 10° N/m² G=80 x 10° N/m²

1. A thin disk attached to the end of an elastic beam has three uncoupled modes of vibration. The longitudinal motion, transverse motion and the torsional oscillations are all kinematically independent. Calculate the following for the system shown. a. Longitudinal stiffness b. Transverse stiffness c. Torsional stiffness 65 cm I r=10 mm E-200 x 10° N/m² G=80 x 10° N/m²

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

Related questions

Q: For what value of k is the steady- state amplitude of angular oscillation of the bar shown in…

A: Draw the free-body diagram of the bar. Draw the free-body diagram of the mass.

Q: 3) A one-degree-of-freedom system has an effective mass M-4-kg, an effective spring stiffness…

A: To find (a) The natural frequency ωn and critical damping ratio ζ (b) The response q as a function…

Q: 2.20. Calculate the frequency of damped oscillation of the system shown in Fig. 2.23 for the values…

A: Answer: The value of critical damping is 35,000 N•s/m.

Q: The following is the equation of free damped vibration of a horizontal rod of length L oscillating…

Q: In a damped single-degree-of-freedom system with a mass of m = 10 kg, stiffness coefficient k = 4000…

Q: Consider a spring-mass system with mass equal to 1 kg, spring constant equal to 25…

A: a. Write the expression for the critical damping coefficient, Here, b is the coefficient of…

Q: (1) A rigid bar (OA)with mass m and length L is simply supported at one end and free at the other…

A: Given: Mass of the rod→m=10 Kg And point mass at the end of the rod→M=50 Kg Stiffness of each…

Q: Please solve this problem by showing the manual calculation and choose the correct answer(SUBJECT:…

A: Given: →m1=1.8 Kg ; →m2=0.7Kg→k1=250 N/m→k2=700 N/m→k3=100 N/m And the give vibration is free…

Q: A 100-kg tumbler produces a harmonic force of magnitude 5000 N. The stiffness coefficient of the…

A: Write the magnitude of harmonic force. F=5000 N Write the stiffness coefficient of the support.…

Q: a) Find the equations of motion for this system. b) What are the natural frequency and damping ratio…

Q: An electrical switch gear is supported by a crane through a steel cable of length 4 m and diameter…

A: Given data: L=4 md=0.01 mT=0.01 s Need to determine the stiffness of the cable.

Q: In this lab, we will observe the free response of a first order mechanical system: a rotating…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Consider the single degree of freedom spring–mass system shown in Fig. where k = 4 x 10$ N/m and m =…

A: Given data Consider the single degree of freedom spring-mass system shown in Fig. where k = 4 x 105…

Q: A machine of mass m is mounted on a vibration isolator as shown in Figure 1. Its transfer unction…

A: 8×s+5s2+10s+16s+40×0.05s2+5 X(s) given Plot of response-

Q: A cantilever is driven in flexural vibration by an electrical coil mounted at its free end and…

Q: For the system below, the mass, m is attached to the end of a cantilever beam of length, l,…

Q: (1) A rigid bar (OA)with mass m and length L is simply supported at one end and free at the other…

A: For solution refer below images.

Q: III) A relatively well-praised model for a car suspension is depicted in Figure 5: 1* 1* Body Mass M…

A: Given:The model of the car suspension is given below;

Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

100%

1. A thin disk attached to the end of an elastic beam has three uncoupled modes of vibration.
The longitudinal motion, transverse motion and the torsional oscillations are all
kinematically independent. Calculate the following for the system shown.
a. Longitudinal stiffness
b. Transverse stiffness
c. Torsional stiffness
mumm
65 cm
r= 10 mm
E-200 x 10° N/m²
G=80 x 10º N/m²

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

For the system shown below, the disc of mass M rolls without slip. Assume that the mass M = 11 kg, the damping constant C - 209 Ns/kg and the stiffnesses K, = 9,036 N/m, K2 = 4,855 N/m, the radius of the disc R = 0.4 m and the moment of inertia of the disc about its centre I = MR² What is the damping ratio of the free vibration of this system? www K2 K1 M *No Slip
Find the natural frequency (in Hertz) of the system illustrated in the following figure. Consider the length of the rigid bar as 2L and assume K1=4,659 N/m, K2=5,977 N/m, M=0.6 kg, L=0.5 m and g=9.81 m/s2.
MECHANICAL VIBRATIONS
(b) A passenger car has a tyre spring rate of 18,900 N/m. The front suspension rate is 1,450 N/m and the rear is 1,050 N/m. Assume the front tyres are loaded to 10,000 N and rear tyres are at 7,900 N. (i) Solve the front suspension ride rate in N/m. (11) Evaluate the natural frequency at front suspension.
Consider the damped mass-spring system for mass of 1.5 kg, spring constant 10 N/m, damping 3 kg/s and an oscillating force 4.7 cos(@t) Newtons. That is, 1.5x" + 3x' + 10x = 4.7 cos(@t). What positive angular frequency o leads to maximum practical resonance? W = help (numbers) What is the maximum displacement of the mass in the steady state solution when the we are at practical resonance: C(@) = help
The logarithmic decrement of damping of a tuning fork oscillating with a frequency 1,1 Hz is 5. After what time interval will the amplitude of the tuning fork oscillations decrease by 7,1 times? Assume that the period of damped oscillations is close to the period of free undamped oscillations.
A concrete part with a mass of 800 kg is hung on a 6 m long steel cable. You determine the spring constant to be 3.924 \times 10 ^ 6 N/m. What is the oscillation period when the steel beam oscillates in the direction of the cable? Provide the result in seconds.
The 1 degree of freedom underdamped vibration system is subjected to external force as shown in the figure. (1) Finding a steady state response. (2) Induce the frequency at which the maximum displacement occurs in detail and (3) Find the maximum displacement at that time. (4) Plotting the frequency response function and explain its concept.
Given an oscillator of mass 2.0kg and spring constant of 180N/m, what is the period without damping? Use numerical methods to model this oscillator with an additional friction force equal to where c is a positive damping constant. Using c=5.0, what is the new period of oscillation. What about for c=10? Assume initial position is 0.2m and initial velocity is zero. Please find the period using the position versus time plot and use the first full cycle of the motion.
III) A relatively well-praised model for a car suspension is depicted in Figure 5: 4 4 Body Mass MW Suspension Mass b₂ ↑" Figure 5 - Model of the suspension of a car. Considering it is a system with two degrees of freedom, WRITE the equations that model the free vibrations of this system.
1
Answer ASAP would be appreciated