kAyтYY - 4B0 =otFigure Q1 A mass, m of 21 kg consider one vertical motion only with angular displacement, 0 =wt, with spring coefficient, k of 10 kN/m as shown in Figure Q1. If the systemoscillates at free motion y = Y sin(@nt) with amplitude, Y of 13 mm:(i)Determine the natural frequency of the system, @n.(ii)Solve the time taken to complete one cycle of motion.(iii)Analyze the velocity of the mass, ý at position A.

Answered: Image /qna-images/answer/742c1e6e-4b62-466f-acfd-714c0a0f6b70.jpg

A mass, m of 2 1 kg consider one vertical motion only with angular displacement, wt, with spring coefficient, k of 10 kN/m as shown in Figure Q1. If the sys oscillates at free motion y = Y sin(@nt) with amplitude, Y of 13 mm: (i) Determine the natural frequency of the system, @n.

A mass, m of 2 1 kg consider one vertical motion only with angular displacement, wt, with spring coefficient, k of 10 kN/m as shown in Figure Q1. If the sys oscillates at free motion y = Y sin(@nt) with amplitude, Y of 13 mm: (i) Determine the natural frequency of the system, @n.

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: 2.20. Calculate the frequency of damped oscillation of the system shown in Fig. 2.23 for the values…

A: Answer: The value of critical damping is 35,000 N•s/m.

Q: Piston (M=5kg) is driven when the fly wheel (r=0.1m, J=0.5kgm^2) moves the arm (L=0.2m,m=1kg). The…

A: Given: To find: Natural frequency

Q: Prob. # 3] A 0.453 kg mass is attached to a spring having static deflection of 7.87 mm. Calculate,…

A: Deflection (∆) =7mm To fund natural frequency of system

Q: Given the vibrating system below: K4 Find the following K3 Y(t) =Ysin30t where fos = 30 and K1…

Q: Please solve this problem by showing the manual calculation and choose the correct answer(SUBJECT:…

A: Given: →m1=1.8 Kg ; →m2=0.7Kg→k1=250 N/m→k2=700 N/m→k3=100 N/m And the give vibration is free…

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

Q: A spring with a mass of 1 kg has a spring constant 43 kg/s2. If the spring begins at equilibrium…

Q: An (a) oscillating block-spring system has a mechanical energy of 2.38 J, an amplitude of 9.52 cm,…

A: Given data, Mechanical Energy= 2.38J Amplitude= 9.52cm Maximum Velocity=2.69m/s

Q: 1. For the system shown, the spring constant k = 400 kN/m, damping coefficient zeta = 0.5 and the…

Q: 4. Consider the system shown below. Let K-2 N/m, C- 2 kg/s, M = 1 kg, x(0)=-0.1 m, and v(0) = 1 m/s.…

A: The mass is .The spring constant is .The damping constant is .The intial condition are .

Q: Consider the following system (m = 27 kg and k=3kN/m). %3D k Suppose that the damping coefficient is…

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

Q: Consider the single degree of freedom spring–mass system shown in Fig. where k = 4 x 10$ N/m and m =…

A: Given data Consider the single degree of freedom spring-mass system shown in Fig. where k = 4 x 105…

Q: Given m = 1 kg, b = 5 Ns/m, k = 4 N/m, and F = 5 N. (a). What is the natural frequency of the…

A: According to the bartleby policy, answering first 3 subparts of the question

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 21 kg consider one vertical motion only with angular displacement, 0 =
wt, with spring coefficient, k of 10 kN/m as shown in Figure Q1. If the system
oscillates at free motion y = Y sin(@nt) with amplitude, Y of 13 mm:
(i)
Determine the natural frequency of the system, @n.
(ii)
Solve the time taken to complete one cycle of motion.
(iii)
Analyze the velocity of the mass, ý 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 by step

Solved in 2 steps with 2 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

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 Ⓒ
Find the natural frequency (in Hertz) of the system illustrated in the following figure. Consider the length of the rigid bar as 2L and assume K1=4,659 N/m, K2=5,977 N/m, M=0.6 kg, L=0.5 m and g=9.81 m/s2.
Find the natural frequency (in Hertz) of the system illustrated in the following figure. Consider the length of the rigid bar as 2L, the mass of the rigid bar as m and assume K1=7,873 N/m, K2=8,185 N/m, M=3 kg, m=3 kg, L=0.5 m and g=9.81 m/s2.
B/ Two massless springs with spring constants k1=100 and k2=150 are attached to mass of (m=20 kg) at A in parallel as shown in Fig (a). An identical pair of springs is attached to mass B in series as shown in Fig (b). Taking mA = mB = m, find and compare the natural frequencies ws and wp and (ws/wp) of the two systems. (b)
Consider the damped mass-spring system for mass of 1.5 kg, spring constant 10 N/m, damping 3 kg/s and an oscillating force 4.7 cos(@t) Newtons. That is, 1.5x" + 3x' + 10x = 4.7 cos(@t). What positive angular frequency o leads to maximum practical resonance? W = help (numbers) What is the maximum displacement of the mass in the steady state solution when the we are at practical resonance: C(@) = help
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.
The figure shows a bar of mass M-4 Kg and length L-1 m, has a concentrated mass at the end of the bar of m= 4 kg. The bar is supported by a pin at O and three springs as shown. In the value k- 800 N/m Find the natural frequency of the system. 2k O 17.0 rad/s O 14.4 rad/s O 10.9 rad/s 20.3 rad/s elle 00000 + 4 1 2 k > bar of mass M mass m
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.
Answer ASAP would be appreciated
Obtain X1(s)/F(s) and then determine the damping coefficient C of the mechanical system below. m2 =160.1 kg, k =953.7 N/m, k, =1,451.7 N/m, b, =148.0 N-s/m. X1(t) x2(t) k2 f2(t) m2 k, b2 massless plate Sonraki
A mass is suspended from a spring and is pulled down 3 cm from equilibrium and released. It completes a period in 2 seconds. Ignoring damping factors, find the function for the displacement from equilibrium h(t) in centimeters t seconds after the mass is released.