Consider the system in Figure 1-a, which is initially at equilibrium. The massless bar AOB with point mass m = 2 kg attached to B rotates with rotational viscous damping coefficient b about the fixed point O. The system is connected by a horizontal spring (acting at B) to a fixed wall. The rotating bar has a length 3L=1.5 meters. L 2L k 17 win A Rotational viscous damping coefficient b B g Massless

Consider the system in Figure 1-a, which is initially at equilibrium. The massless bar AOB with point mass m = 2 kg attached to B rotates with rotational viscous damping coefficient b about the fixed point O. The system is connected by a horizontal spring (acting at B) to a fixed wall. The rotating bar has a length 3L=1.5 meters. L 2L k 17 win A Rotational viscous damping coefficient b B g Massless

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: A mass of one kg stretches a spring 49 cm in equilibrium. It is attached to a dashpot that supplies…

A: From the solution refer below images.

Q: *Need answer only for the a3. Consider a mass spring system with an external force ?(?) = ?osin?o?.…

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: 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: 2. Consider the damped spring-mass system with m 1, k = 5, c = 2, and F(t) = 8 cos ot. (a) Determine…

A: (a).

Q: 1.2Kg is on a plane inclined at 30 degrees for which uc = 0.11. The block is connected to a spring…

Q: A body of mass 14 kg is suspended vertically on a spring and stretches it 49 cm. At t=0, the mass is…

Q: 4.4. A spring-mass system is subjected to a harmonic force which has an amplitude 30N and frequency…

Q: A mass weighing 96 Ib is attached to a spring hanging from the ceiling and comes to rest at its…

A: m=96 lbs F(t)=3 cos 6t lbs k=15 lb/ft c=2 lb-sec/ft g=32 ft/sec2 Now, ωn=1596ωn2=0.15625 and,…

Q: X1 X2 m2 k1 k2

Q: Consider the dynamic system shown below. Jo k₂ M Determine the characteristic equation(s) when a…

A: Determine the characteristics equation?

Q: This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both…

Q: kg object is attached to a spring vwith spring constant 16 kg/s². It is also attached to a dashpot…

Q: The mass (Figure P4), m = 0.4 kg, is suspended from two springs in parallel with stiffness of k1 =…

Q: Q.1 Determine the amplitude of the steady state motion of the mass shown below if o = 200 rad/s. k =…

A: The amplitude of the steady state motion of the mass shown below is given by X=Fs1-ωωn22+2ζωωn2where…

Q: from the pivot point. A mass M = 2 kg is situated at the end of the bar, a further distance b = 0.7…

A: Solution: Given Data: M=2 kgb=0.7 mm=1 kgK1=3 kN/mK2=9 kN/mC=10 N-s/kgF=FocosΩtFo=50 NΩ=34…

Q: Consider the dynamic system shown below. Rod Pulley Rc Rod The following parameters are given for…

Q: For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is…

Q: The car bridge in Figure Q20 can be modelled as a damped-spring oscillator system with mass M =…

A: Given: The mass of the vehicle: →m=1136 Kg Mass of the bridge: →M=10000 Kg Spring constant→k=50000…

Q: 1. Figure 1 shows a rocking mechanism that consists of two masses m₁ and m₂ connected by a rigid and…

A: For the solution refer below images.

Q: Consider a mass-and -spring system containing two masses m1=1 and m2=1 whose displacement functions…

Q: Consider the system in Figure 2 described by Equation 2 and assume there is no damping, b = 0. Let m…

Q: A mass m=4 kg is attached to both a spring with spring constant k= 577 N/m and a dash-pot with…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A spring is attached to the floor. When a 125 g mass is placed on top of the spring it compresses by…

A: Given Mass, m = 125 g Deflection = 0.26 m

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

A: Given:To find:

Q: Figure below shows a rod with mass M = 100 kg, cross section area A = 10 cm². The rod is supported…

A: According to the question data provided in the question M=100kg m=120kg A=10cm2=0.001m2 L=1m f=180Hz…

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

Consider the system in Figure 1-a, which is initially at equilibrium. The massless bar AOB with point mass
m = 2 kg attached to B rotates with rotational viscous damping coefficient b about the fixed point
system is connected by a horizontal spring (acting at B) to a fixed wall. The rotating bar has a length 3L=1.5
meters.
L
2L
k
twine
ww
Figure 1-a
A
Rotational viscous
damping coefficient b
B
g
Massless
a) Write the linearized equation of motion of the system (Figure 1-a) for small angular displacement 0 (t).
(Symbolic)

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Calculation of equation of motion

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 7 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

Whats the first equation (circled) and how did we get it ?
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of F friction We can write the resulting system of second-order DEs as a first-order system, w'(t) = Aw(t), with w = (x₁, x₁, x₂, x₂) T For values of k = 4, m = 1 and c = 21,2 = 0.5±3.2i, V₁ 23,4= - 0.5 ± 1.13i, V3 1, the resulting eigenvalues and eigenvectors of A are -0.039 0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i' 0.409 -0.216 - 0.489i 0.661 and (a) Find a set of initial displacements x₁(0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (x₁(0), x₂(0)) Enter your answer using angle braces, (and ). cx (friction proportional to velocity). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s
Consider the dynamic system shown below. Jo k₂ M Determine the characteristic equation(s) when a torque equal to r(t) is applied to the double pulley.
P
A block of mass m = 1.2Kg is on a plane %3D inclined at 30 degrees for which uc = 0.11. The block is connected to a spring of constant K = 3.2 N / m, by a rope passing, without slipping, by a pulley. The pulley is a disc of 0.8Kg and 0.14m radius. If the system is initially at rest and the spring has zero elongation, what is the block velocity modulus when the block has slid 0.25m down the inclined plane? k=3,2 N/m 130° A Figure 11.75
Please don't provide handwritten solution .....
3) Consider this car, which can be modelled as a rigid bar with its centre of mass C.G. not coinciding with its geometric centre (m= 1000kg, 11m; /2 = 1.5m ), and supported by two springs, k = kx=20kN/m, as shown in Figure Q1 (a) Describe the system in term of degree of freedoms (b) Draw the free body diagram for the system to derive the equations of the vibration motion (c) Determine the mass matrix and stiffness matrix of the system. (d) Determine the nature frequencies of the system Bounce C.G. Pitch -1/2- Figure Q1
F(1) Spring m. Ball Dashpot Find the motion of the mass-spring system with the driving force F(t) shown above for the given data. [Hint: Read Forced Oscillations notes.] e-2t, 0 2 y(0) = 1, y'(0) =-1.5.
Please asap
Consider the pictured mass-spring system excited by a mov- ing base y(t) and with a drag force = -e times the velocity of the mass relative to the lab. Find the steady state motion x(t) = X (t) – Xeg representing the displacement from equi- librium (X = natural spring length) relative to the moving base when the cart's motion is sinusoidal y(t) = Y, sin(wt). y(t) (given) X(t) k There are two stages to this problem: a) Derivation of the differential equation. It should come out the form indicated here: Meffë + Ceffå + KeffT = Dÿ+ Eÿ You are advised to use F = ma to derive it. The sum of the forces has two terms, with magnitudes: k times the stretch of the spring, and e times the velocity of the mass relative to the lab. Be careful in your derivation: x and X represent motion relative to the moving base; the mass's acceleration in the frame of the lab is therefore NOT d²r/dt, nor is its velocity relative to the lab equal to dr/dt (think about the position of the mass as described from…
m2 Two masses connected by a massless string of length I slide without friction on two inclined planes as shown in the figure above. The motion is restricted to the x-y plane indicated in the figure. Gravity is acting in the negative y-direction. (a). Explain the term "virtual displacement". (b). State d'Alembert's principle of virtual work. (c). Write down d'Alemberts equation for this system in cartesian coordinates. Need detailed and step by step answer of all subparts with good handwriting Please I want to learn
answer ASAP would be appreciated