Q6. For the system as shown where the supporting surface is frictionless and I= 0.5mr², ww 2m (1, r) (1) derive the equations of motion using Lagrange equation method, (2) find its natural frequencies, and (3) determine the associated mode shapes.

Q6. For the system as shown where the supporting surface is frictionless and I= 0.5mr², ww 2m (1, r) (1) derive the equations of motion using Lagrange equation method, (2) find its natural frequencies, and (3) determine the associated mode shapes.

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: elapse before the amplitude of the free vibration 2.22 A one-degree-of-freedom system has an…

Q: Q.2 For the system shown; a- Derive the equations of motion using Lagrange method (use the…

A: To Find: A. The equation of motion using Lagrangian B.Natural Frequancy…

Q: The answer for natural frequency is given below. Obtain the differential equation of motion and…

A: From the similar triangle-δ1l1=δ3l3δ1=l1l3δ3 .....(1)Similarly,δ2l2=δ3l3δ2=l2l3δ3 .....(2)

Q: Consider a spring–mass–damper system with m = 80 kg, c = 15 kg/s, and k = 1500 N/m with an impulse…

A: Given Spring constant, k = 1500 N/m Mass, m = 80 kg Damping coefficient,…

Q: A mass-spring system is driven by the external force S-2, 0 <t < 5 g(t) = 2, 5 <t< 10' 9(t + 10) =…

Q: The frequency of a damped harmonic oscillator is one-half the frequency of the same oscillator with…

A: Natural frequency: The number of vibrations executed by a body when it is vibrating freely in one…

Q: The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 3 mm.…

Q: 2DOF system as shown in figure below, M1=m, M2=2m, k1 =5k, k2=10k. 4. If initial displacement of m1…

Q: Piston (M=5kg) is driven when the fly wheel (r=0.1m, J=0.5kgm^2) moves the arm (L=0.2m,m=1kg). The…

A: Given: To find: Natural frequency

Q: A mass attached to a spring is initially (t=0) released 5cm away from the equlibrium position. What…

Q: A vehicle wheel, tire, and suspension can be modeled as a SDOF spring and mass as depicted below:…

A: Given data: The mass of wheel and tire is m=300 kg The frequency of oscillation is ω=10 rad/s

Q: system of Volvo articulated dump truck is to be modelled mathematically given the following data:…

Q: An automobile is found to have a natural frequency of 2 rod per seconds without passengers and 17.32…

Q: The underdamped spring-mass system of m = 120 kg mass, stiffness of k = 3,080 N/m. and damping…

Q: 4.a Draw the free body diagrams and derive the equation of motion.

A: 1. Two Masses-Two Springs system of vibration 2. All spring constants are equal i.e., k1 = k2 = k3 =…

Q: 2) A block of mass m is attached to a spring with force constant, k and oscillate at a frequency f.…

A: The initial frequency of the spring-mass system is given as, f=12πkm Here, k, and m represent spring…

Q: 2DOF system as shown in figure below, M1=m, M2=2m, k1 =5k, k2=10k. 4. If initial displacement of m1…

Q: Figure Q1 shows a three-degree-of-freedom spring-mass system. If all the masses move to the right…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Q.5 The rotating unbalance of a 185 kg machine is 0.65 kg.m. The machine is paced at the midspan of…

Q: A mass of 10kg is attached between two spring having stiffness 15KN/m & 10kN/m respectively.The…

A: Data given- Mass m = 10 kg Stifness k1 = 15 kN / m k2 = 10 kN /m

Q: Problem 6: An object of mass 2 kg is attached to a spring of stiffness 200 N/m on a horizontal…

Q: Consider the damped harmonic oscillator shown below and modeled by the system: k - ()*+ (-) m (1)…

Q: 3 Consider the following 1-DOF system, where k = 857.8 N/m, c =7.8 kg/s, and m - 19.2 × 10-3 kg,…

Q: For the mechanical system shown, a- Find the equivalent mass, equivalent spring stiffness and…

Q: When spinning at 500 rotations per minute two washing machines produce two sinusoidal forces with…

A: Given Data: washing machines rotation n=500 rpm Two sinusoidal forces with same maximum amplitude…

Q: Q4\Find the type of damping in this system Where: m=5kg, K = 1500 Nm Damping coefficient= 1.5 *105…

A: In this problem, it is asking whether the system is underdamped, critically damped, or overdamped.…

Q: A 65 kg painted sewing machine has an imbalance value of 0.15 kgm in rotation. The machine operates…

Q: A mass-spring system is driven by the external force S-2, 0 <t < 5 g(t) = %3D 2. 5sts 10'g(t + 10) =…

Q: as shown in figure below, M1=m, M2=2m, k1 =5k, k2=10k. Set the mode shapes of the system. Finitial…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: Given : Amplitude, A = 0.1 m In Simple Harmonic Motion, The motion of the mass-spring system…

Q: n object of mass 2 kg is attached to a spring of stiffness 200 N / m on a horizontal frictionless…

A: Frequency is given by,ω=kmω=2002ω=10 radian/s

Q: Consider the damped mass-spring system for mass of 1.5 kg, spring constant 10 N/m, lamping 3 kg/s…

Q: Consider a driven undamped spring/mass system described by the initial-value problem d²x + w²x =…

A: Solution: Given Data: d2xdt2+ω2x=Fosinnγtx0=0dx0dt=0 To Find:

Q: Q2: For a system the equations of motion are as shown below, find frequencies and mode shapes. Ţ…

Q: Q2: k= 10 kg/cm m= 8 kg Determine the natural frequency and the k motion equation of the system…

Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

100%

Q6. For the system as shown where the supporting surface
is frictionless and I = 0.5mr,
2m
(I, r)
(1) derive the equations of motion using Lagrange equation
method,
(2) find its natural frequencies, and
(3) determine the associated mode shapes.
m T
X2

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 5

Step 6

Step 7

Step 8

Step by step

Solved in 8 steps

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 vibrometer with mass (2kg) & spring stiffness (k), base excitation y(t)=b sin(wt), itation frequency=5Hz, 2Z=24mm & zeta=0.2, frequency ratio (r)=2, find: ● Wn. K. ● ● ● Amplitude ratio Z/Y. b & delta. 2 kg Structure. W D 24 mm
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.
H.W 2.pdf > H.W: 1. For the system shown below, if the mass is 10kg and the stiffness of the spring is 1000N/m, drive the general oscillation equation of the system with a, = 0.1 mm for the following initial conditions: • Casel: y(0) = 0.1 mm & y(0) = 0 • Case2: y(0) = 0.1 mm & y(0) = 10 m/s • Case3: y(0) = 0.1 mm & y(0) = -10 m/s LUnstretched spring System at rest System in motion 2. Use any software to draw the general solution of the oscillation system for the three initial condition cases Iwwww.ojl. www.pi
Do not copy
a damper, the frequency of oscillation is found to the stiffness of the spring is 1 kN/m. By introducing coefficient of the damper? be 90% of the original value. What is the damping In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing be 90% of the original value. What is the damping (a) 1.2 Ns/m (b) 3.4 Ns/m (c) 8.7 Ns/m (d) 12.0 Ns/m
Question 4 A light aircraft nose landing gear is to be simply modelled as masses and springs illustrated in Fig. 3. The stiffness and mass of the tyre is given by k2 and m2 respectfully. The stiffness of the landing gear is given by kl and the mass of the aircraft by mi. There is no damping and it is only free to vibrate in the vertical direction. Write the equation of motion for this system in matrix form. Calculate the natural frequencies if the following values are given kı=10* N/m, k:=10³ N/m, mi-2000kg and m2 = 50kg. c) Determine the modal matrix to solve this problem. Fig. 3 Nose landing gear and Model XI X2 kı k₂ mi m2
Nilo
Suppose that a horizontal string of length c =2 with fixed end points (the end points are fixed on the horizontal axis) is initially raised at its mid point to the height h above the horizontal and then released (no initial velocity). Write the boundary value problem modeling the vibrations of the string and solve the problem.
O O O O O Clear selection A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with an amplitude A=0.1 m. At what position (x=?) would the kinetic energy of the system be equal to three times its elastic potential energy (K = 3U)? O At x = +0,025 m O At x = +0.1 m O At x = +0.08 m O At x = +0.04 m At x = +0.05 m A block of mass m = 5 Kg is attached to a spring of spring constant k. The block oscillates in simple harmonic motion on a frictionless horizontal surface. The
H6.