Consider the two-degrees-of-freedom mass-spring system below. Assume m₁ = 30 kg, m2 = 35 kg. If the second natural frequency of the system is 100 rad/s, the value of stiffness k is k₂ = k k₂= k k₂= k 174.41 kN/m 107.38 kN/m MA 140.93 kN/m 39.24 kN/m 73.62 kN/m 4 4 x₁ (t) x₂ (t) m₂ m₂ mm

Consider the two-degrees-of-freedom mass-spring system below. Assume m₁ = 30 kg, m2 = 35 kg. If the second natural frequency of the system is 100 rad/s, the value of stiffness k is k₂ = k k₂= k k₂= k 174.41 kN/m 107.38 kN/m MA 140.93 kN/m 39.24 kN/m 73.62 kN/m 4 4 x₁ (t) x₂ (t) m₂ m₂ mm

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: The differential equation of motion The maximum displacement and the time of its occurrence.

Q: relative to M3. Both springs are undeflected when x₁ = x₂ = 0. Draw free-body diagrams and write the…

Q: . What is the energy stored in the spring if the spring iscompressed 0.5 m?

A: Given data mass = 40 kgspring constant = 3000 N/mCompressed length = 0.5 mWe have to find the energy…

Q: 1. Two carts with negligible rolling friction are connected as shown in Figure 1. An input force…

A: Step 1: Step 2: Step 3: Step 4:

Q: A block 4, of mass m is connected through a cable and a pulley to an elastic spring (see figure…

A: Given data: k=100 N/mθ=45°m=85 kg Need to determine the distance covered by the block when it stops…

Q: Q1 ( k₁=1500 N m For the system shown in Figure 1, m₁ = 35 kg, m₂ = 20 kg, N and k2=2000 If the…

A: The values are m1=35 kg, m2=20 kg, k1=1500 N/m, k2=2000 N/m. The initial conditions of mass m1 is…

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: Consider a mass-spring system shown below. X1 m The system model is given by m 1 2 k₁ 00000 d₁2 m₁…

Q: A railroad bumper is designed as a spring in parallel with a viscous damper. What is the bumper's…

Q: A slider of mass 1 kg travels in a cylinder with a velocity 80 m/s and engages a spring - damper…

Q: X1 X2 m2 k1 k2

Q: pring stiffness k = 2700 N/m, and a damping coefficient e = 18 N-s/m. The ss is subjected to a…

Q: Q4. A two-degree-of-freedom model consisting of two masses connected in series by two springs is…

Q: A 25 kg mass is attached to a spring with spring constant 100 N/m. The mass is driven by an external…

Q: ad is described by the function here the boldface type indicates that G is a vector. a) Draw an FBD…

Q: When testing the landing gear unit of a space vehicle drop tests are carried out. Figure 2.17 is a…

Q: An air compressor weighs 4450 N and is operating at a constant angular speed of 1750 rev/min. The…

A: Given data:

Q: 3.33. The following data are given for a damped single degree of freedom mass-spring system: mass m…

Q: Figure 1 below depicts the popular Spring-Mass-Damper system in which m is the mass, c represented…

A: Mass, m=20 kgDamper coeffiecient, c=20 Ns/mSpring constant, k=4000 N/mPeriodic harmonic force,…

Q: A box with a mass of 3m is on frictionless ground, attached to a wall (on the left-side of the box)…

A: Given: To find: Equations Stiffness and mass matrix Normal frequencies Motion of the masses

Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

Consider the two-degrees-of-freedom mass-spring system below. Assume m₁ = 30 kg, m2 = 35 kg. If the second natural frequency of the system is 100 rad/s, the value of
stiffness k is
www.
k₁=k
k₂ = k
k3= k
174.41 kN/m
107.38 kN/m
140.93 kN/m
39.24 kN/m
73.62 kN/m
Next
000 00
Previous
4
x₁ (t)
x₂ (t)
m₁
m₂.
mm

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 4 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

4. A spring with stiffness constant k = 2000 N/m attached to a platform launched a mass of 2kg vertically in the air to some maximum height (measured from the equilibrium point of the spring). The spring was compressed by 0.3 meters before launch. Due to internal friction of the spring, 10 Joules of energy was lost as the spring expanded. How fast was the mass travelling when it was at half of its maximum height? You must use g= 10m/s? for this problem or you will actually find it much more difficult to calculate. Hint: First solve the problem of finding what the maximum height is and then solve the problem of finding the speed at half of that height.
answer would be much appreciated
The 20-kg block is subjected to the action of the harmonic force F = (90 cos 6t) N, where t is in seconds. (Figure 1) Figure k-400 N/m Sw 20 kg k=400 N/m 00 F-90 cos 6r c-125 N-s/m < 1 of 1 Part A Write the equation which describes the steady-state motion. Express your answer in terms of t. Express your answer using three significant figures. Express the phase radians and the final result in meters. ΠΙΑΣΦ 4 ? m
Please write explanation and don't use the calculator.(Math differential equation) 1. Consider a damped spring-mass system with ? = 1kg, ? = 4 kg/s^2 and ? = 5 kg/s.a. Write the equation of motion (the differential equation) for this systemb. Find the general solution?(?) =c. Solve the initial value problem if ?(0) = 1 and ?′(0) = 0?(?)
A machine is supported on four steel springs. By neglecting damping, the natural frequency of vertical vibration the machine-spring system runs at f=200 cycles per minute. The machine generates a vertical force p(t)=posinot. When the machine runs at f₁ =30 cycle per minute the amplitude of vertical vibration is measured as u₁=0.2cm, at f₂=170 cycle per minute is u₂=1.042cm, and at f3-400 cycle per minute is u3=0.0248cm. Calculate the amplitude of vertical motion of the machine if the steel springs are replaced by four rubber isolators which provide the same stiffness, but introduce damping equivalent to -0.25 for the system. Evaluate the response of the system for frequency ratios r, respectively.
Please and thank
Please solve only 4,5
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
The shaft in the figure, carrying three unbalanced masses, is rotating at a constant speed hızla = 10 r / s. Find the balancing values (kg.mm) and their positions in case of balancing in DI and DII planes.
Q4. A two-degree-of-freedom model consisting of two masses connected in series by two springs is shown in the figure below. The physical parameters have the values m, = 8 kg, m, = 2 kg, k, = 20 N/m, and k2 = 30 N/m. X1 X2 m1 m2 k1 k2 (A) Write down the equation of motion for mass m, (B) Write down the equation of motion for mass m, Calculate the first (larger) natural frequency of the system (D) Calculate the second (smaller) natural frequency of the system
In the system shown in the figure, the spring stiffness k = 2 × 103 N/m and the total massof the system is m = 20 kg, the eccentric mass m0 = 0.2 kg, the eccentricity e = 0.1 m andthe rotation angular velocity of the unbalanced mass is ω1 = 20 rad/s. The applied force isF(t) = 15 sin ω2t with ω2 = 30 rad/s. Determine:(a) the steady state motion of the system;(b) the force transmitted in the spring and estimate the maximum value of the force
A 20 kg weight is attached to a spring with constant k = 320 kg/m and subjected to an external force F(t) = 1200 cos(2t). The weight begins at rest in its equilibrium position. Find its displacement for t> 0, with y(t) measured positive upwards. y(t) =