Q.2Two springs, damper and a mass are attached to a rigid, weightless bar PQ as shownbelow.Write the equation of motion of the system using D'Alemberts principle.Find the natural frequency of vibration of the system.J6+ (kde) ds.C0000m

Two springs, damper and a mass are attached to a rigid, weightless PQ bar as shown below.Write the…

Answered: Q.2 Two springs, damper and a mass are…

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

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Big and clear handwriting with all the steps please . Make sure calculations and answers are accurate please. THANK YOU
PLs see the question in the attached file.
QI Calculate the frequency of damped oscillation of the system shown in Figure () for the value m = 1.75 kg,c 350 N. s /m, k =7 x 107 N Am, a = 1.25 m and b = 2.5 m. If the mass pulled down 10' find the response of the system after cycle. I, mb² rigid link
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
PARTS A & B solve carefully and label each part and CIRCLE FINAL ANSWER ( Use image Below) Part A - Assuming the elements are all linear, determine a model for the mass-spring-damper system. Make sure to clearly define the direction of positive velocity. Simplify your answer such that the model is in terms of the parameters (?, ?, ??, ??), the input force (?), the spring deflection and the mass velocity as well as their time derivatives. Part B - Take the ANSWER from PART A and replace the damping constant ? with the nonlinear expression ? = ?? + ?? + ? , with ? as the velocity of the mass.
A pump of mass 30 kg is supported on a support structure which has 4 springsarranged in parallel with stiffness values of 10 kN/m, 15 kN/m, 8 kN/m and12 kN/m respectively. Viscous damping is present within the system and 1 kNs/mis applied by a damper.i) Produce a neat sketch of the system and state its equation of motion.ii) Determine the damping ratio for the system, commenting on its value. iii) Determine the damped frequency of vibration.iv) Determine the logarithmic decrement for the vibrating system.
4 QUESTION 20 The car bridge in Figure Q20 can be modelled as a damped-spring oscillator system with mass M = 10000 kg, spring coefficient k = 50000 N-m-1 and damping constant c = 50000 N-s-m-1. Cars cross the bridge in a periodic manner such that the bridge experiences a vertical force F (N) expressed by F = mg sin(10t) where m = 1136 kg is the average mass of passing cars, g = 9.81 m-s-2 is the gravitational acceleration and t (s) is the time. Determine the maximum force magnitude transmitted to the foundation (see Figure Q20) during the steady-state oscillatory response of the system. Provide only the numerical value (in Newtons) to zero decimal places and do not include the units in the answer box. E m M foundation Figure Q20: Vibrating car bridge.
The motion of a spring-mass system with damping is governed by: (see image) (a) Classify the damping as either undamped, underdamped, critically damped, or overdamped. (b) Find the general solution of the system and specify the amplitude, frequency and phase shift. (c) Solve the initial value problem
2. Calculate the natural frequency and damping ratio for the system in figure below given the values m = 10 kg, c = 100 kg/s, k₁ 4000 N/m, k2 200 N/m, and k3 1000 N/m. = Assume that no friction acts on the rollers. Is the system overdamped, critically damped, or underdamped? C кий m k₂ k3
1- Two mass-spring-damper systems A & B. System A has = 0.1 and @n = 20 rad/sec, and system B has < = 0.3 and wn = 5 rad/sec. Which system will vibrate longer in time? Why?

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Q.2 Two springs, damper and a mass are attached to a rigid, weightless bar PQ as shown below. Write the equation of motion of the system using D'Alemberts principle. Find the natural frequency of vibration of the system. Je* (kde) d. C 0000