The 8kg body is moved to the right of the equilibrium position and released from rest at time t = 0. The viscous damping coefficient is 23NS/mand the spring stiffness, K is 38N/m. Determine the damping factor (ratio) of the system.Note: Give your answer to 3 decimal places.Other Parameters:Logarithmic Decrement (8):Answer:2ng2T C8 = In = In1 = 5 wnTd = 5wnX2Xn+11-5wa 2mkDamping Ratio (5): 5=2vkm2mnV(21)2+8Frequency of damped vibration (wa): wa =1-WnUndamped Forced Vibration:Frequency Ratio (): r-Xp-x sin w tNext pageHous pageType here to search stiffness, K is 38N/m. Determine the damping factor (ratio) of the system.r answer to 3 decimal places.Other Parameters:Logarithmic Decrement (õ):Answer:2m2m. C8 = InnIn1 = ( WnTd@12mXn+11-5Damping Ratio (5): 5 =-v(2m)+62Ce 2ykm2m@nFrequency of damped vibration (wa); wa =Undamped Forced Vibration:Fo/kXp=x sin w t1-)Frequency Ratio (r): r =wnII

Given : m=8 kgc=23 Ns/mk=38 N/m

The 8kg body is moved to the right of the equilibrium position and released from rest at time t = 0. The viscous damping coefficient is 23NS/m and the spring stiffness, K is 38N/m. Determine the damping factor (ratio) of the system. Note: Give your answer to 3 decimal places. Other Parameters: C Logarithmic Decrement (6): Answer: 2ng 2n c 2n 8 = In = 1 In wnTa = 5wn %3D %3D wa 2m X2 Xn+1 !! Damping Ratio (5): 5 = %3D k J(2m)+8 2vkm 2mn Frequency of damped vibration (wa): wa-

The 8kg body is moved to the right of the equilibrium position and released from rest at time t = 0. The viscous damping coefficient is 23NS/m and the spring stiffness, K is 38N/m. Determine the damping factor (ratio) of the system. Note: Give your answer to 3 decimal places. Other Parameters: C Logarithmic Decrement (6): Answer: 2ng 2n c 2n 8 = In = 1 In wnTa = 5wn %3D %3D wa 2m X2 Xn+1 !! Damping Ratio (5): 5 = %3D k J(2m)+8 2vkm 2mn Frequency of damped vibration (wa): wa-

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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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

The 8kg body is moved to the right of the equilibrium position and released from rest at time t = 0. The viscous damping coefficient is 23NS/m
and the spring stiffness, K is 38N/m. Determine the damping factor (ratio) of the system.
Note: Give your answer to 3 decimal places.
Other Parameters:
Logarithmic Decrement (8):
Answer:
2ng
2T C
8 = In = In1 = 5 wnTd = 5wn
X2
Xn+1
1-5
wa 2m
k
Damping Ratio (5): 5=
2vkm
2mn
V(21)2+8
Frequency of damped vibration (wa): wa =
1-Wn
Undamped Forced Vibration:
Frequency Ratio (): r-
Xp-x sin w t
Next page
Hous page
Type here to search

stiffness, K is 38N/m. Determine the damping factor (ratio) of the system.
r answer to 3 decimal places.
Other Parameters:
Logarithmic Decrement (õ):
Answer:
2m
2m. C
8 = In
n
In
1 = ( WnTd
@12m
Xn+1
1-5
Damping Ratio (5): 5 =-
v(2m)+62
Ce 2ykm
2m@n
Frequency of damped vibration (wa); wa =
Undamped Forced Vibration:
Fo/k
Xp=x sin w t
1-)
Frequency Ratio (r): r =
wn
II

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The mass of the system shown below is 10Kg. The mass is initially at rest when at time t=0, it is given an initial disturbance as shown. The viscous damping coefficient is 100NS/m and the spring stiffness, K is 100N/m. Which equation describes the movement of the mass. Disturbance Mess Spring Damper Select one: x(t) = A,e(-3+v??-1 )wnt + + A,e(-3-v²-1 )wnt a. %D O b. x(t) = (A, + A,t) e¯wnt %3D x = (A3cos wat+ A4sin wat)e-wnt Oc. %3D Next page ious page OType here to search
Question 2: a. Determine the differential equation of motion and find the natural frequency (w). Also establish the critical damping for the system shown in Fig. 2a b. If the system has a mass of 0.907 kg with spring stiffness of 7.0 N/cm. Determine the critical damping coefficient.
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.
Number 8 please
7) just solve i - ii Please answer in legible and orderly handwriting. If it is not legible, I will not give a positive rating.
answer quickly
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The mass of the system shown below is 10Kg. The mass is initially at rest when at time t=0, it is given an initial disturbance as shown. The viscous damping coefficient is 100NS/m and the spring stiffness, K is 100N/m. Which equation describes the movement of the mass. Disturbance Mass Spring Damper Select one: x(t) = (A, + A½t) e¯wnt a. %3D x(t) = A, e(-3+v?-1)wnt + A,e(-3-v?-1 )wnt x = (A3cos wat+ A4sin wat)e-wnt %3D C. Finish attempt.. evious page
(note: for this problem do a hand calculation from t = 0 – 5 s , the rest use excel)
Mechanical Vibration. Help fast
Number four, keep four decimal places Number four, keep four decimal places Number four, keep four decimal places
Consider the vibration isolation problem from base excitation. Instead of modeling the isolator as a spring and damper placed parallel to each other, model the isolator using the standard linear model. k m base k₁ motion Develop an expression for the displacement transmissibility of the isolator in terms of the normalized forcing frequency, damping ratio, and the ratio of the two spring constants: y = k₁/k Discuss the influence of the stiffness ratio on the performance of the isolator. For a damping ratio of 0.01 and stiffness ratio of 0.05, use the transmissibility curve to find the effective damping ratio of the isolator (this is equivalent to having a spring and damper in parallel). Can the equivalent damping ratio reproduce the transmissibility curve accurately? Discuss. Provide one specific application where it is necessary to use the standard linear model.