A mass, m of 22 kg consider one vertical motion only with angular displacement, 0wt, with spring coefficient, k of 13 kN/m as shown in Figure Ql. If the systemocillates at free motion y = Y sin(@nt) with amplitude, Y of 19. mm:aAnalyze the acceleration of the mass, ÿ at position A.bExamine the time taken at position A. AyYY - 4B9 =otFigure Q1

Answered: Image /qna-images/answer/d7be2b6e-0f8a-44e9-997f-4d9fbd6f07e6.jpg

A mass, m of 22 kg consider one vertical motion only with angular displacement, 0 = wt, with spring coefficient, k of 13 kN/m as shown in Figure Ql. If the system oscillates at free motion y = Y sin(@nt) with amplitude, Y of 19. mm: a Analyze the acceleration of the mass, ÿ at position A. b Examine the time taken at position A.

A mass, m of 22 kg consider one vertical motion only with angular displacement, 0 = wt, with spring coefficient, k of 13 kN/m as shown in Figure Ql. If the system oscillates at free motion y = Y sin(@nt) with amplitude, Y of 19. mm: a Analyze the acceleration of the mass, ÿ at position A. b Examine the time taken at position A.

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: 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: O f =9f A block attached to a spring. oscillates on a frictionless horizontal surface with a period…

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: Consider a single-degree-of-freedom system with the following equation of motion. m² + c²+kz=0 In…

A: Given: k=15 N/mx1=2 mmx2=1 mmTd=3s Solution: The Logarithmic Decrement is defined as :…

Q: A mass of 3kg stretches a spring from its naturał length of 8.3°cm; to a length of 13,2cm.The mass…

Q: The period ra of damped linear oscillation for a certain 0.7 kg mass is 0.25 s. If the stiffness of…

Q: The dynamic system below has the following parameters: m₁ = 20 kg, m₂ = 15 kg, m3 = 10 kg, k₁ = 100…

A: Given:To find:Mathematical modelTransfer functionState space representation

Q: A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from…

Q: A mass weighing 16 pounds stretches a spring 83 feet. The mass is initially released from rest from…

Q: For the mass-damper system at right, the model in terms of velocity is mv + cv = f. The time…

A: Solution: Given Data: mv.+cv=fτ=mc To Find: Depend-ness of the time constant on the damping.

Q: A mass weighing 16 pounds stretches a spring 83 feet. The mass is initially released from rest from…

Q: X1 X2 m2 k1 k2

Q: 2- Two mass-spring syst the mass of system B answer with a plot

Q: 5. For a simple seismograph as shown in Figure Q5 below, the co-ordinate X₁ measures horizontal…

A: Here, The mass m=1 kg. The spring stiffness k=10 Nm-1. The coefficient of the damper, c=2Nsm-1.…

Q: 6. Consider the following model for a mechanical dynamic system consisting of a two linear springs…

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

Q: Derive the Lagrange's Equations of motion for the system shown in Fig. 1 using the displacement x as…

A: For solution refer below images.

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

Q: A .6kg block is hung from a spring with a force constant of 25 N/m. Calculate the displacement of…

A: Data given - Mass of the block = 0.6 kg Force constant k = 25 N/m

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

A mass, m of 22 kg consider one vertical motion only with angular displacement, 0
wt, with spring coefficient, k of 13 kN/m as shown in Figure Ql. If the system
ocillates at free motion y = Y sin(@nt) with amplitude, Y of 19. mm:
a
Analyze the acceleration of the mass, ÿ at position A.
b
Examine the time taken at position A.

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

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 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

Two identical thin bars, each of mass m and length L, are welded together at a right angle as shown in figure 1. This T-shaped assembly is pinned to ground at point 0. Block B is given a prescribed forced displacement xg = b sin øt. Friction and damping are neglected. a) Derive the equation of motion for the system in terms of the angular position of the bars, 6, and parameters m, L, k, and g; b) Derive an expression for the natural frequency of the system; c) Derive an expression for the forced angular response of the system; L/2 L/2 L Хв
For the mechanical system shown, a- Find the equivalent mass, equivalent spring stiffness and equivalent damping coefficient when x (the displacement of the 2 kg block) is used as the generalized coordinate. b- Derive the equation of motion of the system in terms of equivalent system parameters (equivalent mass, equivalent spring stiffness and equivalent damping coefficient). 3000 N/m 2 kg 200 N.s/m /=0.04 kg-m² r = 10 cm 1000 N/m 1 kg I' 400 N.s/m ial
Q4-6 please
A 2 DOF mass-spring system shown below with n = 1, k = 8, and m initial conditions 2₁ (0) = 1, 2₂(0) = 0, ₁ (0) = 0, and ₂(0) = 1. (a) Find the natural frequencies and normalized modal matrix [X] for the system. T x₁ (1) (b) Using modal analysis and the Cartesian solution form, find the free vibration re- sponse of the system x₁(t) and x2(t). Ţ x2₂ (1) www. 00000 = m m₁ = 00000 k₁ = k 00000 k₂ = nk m₂ = m k3= k = 2 DOF mass-spring system. 2 with the
t. Design the following application case The mechanical vibration system is shown in Figure (a). When a step input with 3N amplitude is subjected to this system, the movement rule of the mass m is shown in Figure (b). Evaluate the values of mass m, damping constant c and spring constant k. m (a) F-3N XX 1.0 x(1)(cm) 0 2 (b) M,-0.095 Ⓒ
3
A damping machine with vibratory system is to be designed with following parameters . K= 100N/m, C=2 N-sec/m, M=1kg Find (i) Decrease of amplitude from its starting value after complete oscillations (ii) The frequency of oscillation
damping, c Sliding Crate with Bumper Stop A crate of mass m enters a lubricated slide at a loading dock with a velocity v, to the right and an initial position x(0) = x, in the diagram shown above. The sliding motion is lubricated, characterized by a linear damping coefficient C. At a distance x = L the crate contacts a bumper stop characterized by a spring constant k and a damping coefficient c. Numerical values for the system parameters are: C = 8 N-s/m k = 1000 N/m m = 50 kg X = 0 Vo = 5 m/s L= 20 m Ca is to be experimentally determined in completing this assignment Bumper: Assignment 1) Given these parameters, determine the governing dynamic equation for the crate position. 2) Convert the governing equation to state variable form. This requires two first-order equations: a. dv/dt f:(x,v) b. dx/dt = f.(x,v) where f, is a function of the states, x and v. where f, is a different function of the states, x and v. Make two sets of the above equations, one each depending on whether there…
Consider the dynamic system shown below. Rod Pulley Rc Rod Pulley RA = 10 cm PIB 1A The following parameters are given for the system: m₂ = 1 kg RA mg mc 2 kg RB Rc 20 cm m₂ = 3 kg R₂ = 30 cm k = 1200 N/m Note that pulleys A and B are constrained to move together and pulleys C and D are constrained to move together. Useful note... a. Obtain the characteristic equation(s) for this system. b. The applied force is removed. Then, pulley A/B is turned 2 degrees and released from rest. Find the system response.
k 0.5m 1m The figure shows a slender rod with a mass of 6 kg. Attached to the rod is a spring of stiffness k = 250 N/m.Amoveable point mass m1 = 1 kg is position at a distance X from the pivot point. You can assume small angle oscillations from the equilibrium position shown in the figure. Calculate the required position, X, of the moveable point mass m1 needed to give the system a natural frequency of 5.3 rad/s. Give your answer to two decimal places.
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.
(note: for this problem do a hand calculation from t = 0 – 5 s , the rest use excel)