3. Please see attached pic. Q3. For the system shown in Figure 3, (i) derive the equation of motion using energy method; (ii)determine the damped natural frequency and damping ratio; (iii) state whether the system isunderdamped, overdamped or critically damped; (iv) determine 0(t) for the given initial conditions.e30 cmXE10 cm40 kg5 kg3.2 × 104 N/m0.3 kg-m²6(0) = 0(0) = 2.5 rad/s150 N s/m

Step 1:Derive the Equation of Motion using the Energy MethodThe system has rotational and…

Answered: Q3. For the system shown in Figure 3,…

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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See the attached image. Please provide the solution modeled as a differential equation. Include an equation of motion of the mass for both no damping force and a damping resistance equal to half the velocity (please notate and show how to identify the velocity) with detailed steps and explanation of the solution.
Vibration Engineering. Please help to provide solution for the problem below. Thank you.
1) For the mass-damper system at right, the model in terms of velocity is mv + cv = f. The time constant of this first order system is t = m/c. For this system, a larger value of the damping constant c causes the time constant to decrease - which is counterintuitive. It seems that a small amount of damping should correspond to a system with a fast response. How can you reconcile this? m CA
The answer should be in Handwritten format.
Please solve the question attached below, Thank You!
Please answer question number 1.
Consider the spring mass damper system shown below. k m x(t) The forces of the spring and damper are represented by Fspring = -kx and Fdamper = -bx' respectively, where k is the spring constant and b is the damping coefficient. The mass has an initial displacement +1 m and velocity 0 m/s. 1. Use Newton's 2nd Law of Motion to derive an ODE to describe the mass's motion. 2. Find x (t) for m = 2 kg, b = 1 N s/m and k = {0.1,0.3,0.5} N. m. What happens when the stiffness of the spring is being increased?
An undamped simple harmonic oscillator has mass 2.0 kg and spring constant 50 N/m. The initial displacement from equilibrium (at time t = 0) is 0.30 m and the initial velocity is 2.0 m/s. %3D 1. Determine the angular frequency (in rad/s), the frequency (in Hz), and the period (in s). Determine numerical values (not in terms of .) Determine the displacement in the form x(t) = Acos(mot) + Bsin(@ot). That is, solve for A and B in meters, and write oo in radians per second.
Please help. This problem involves a mass spring damper system. Thank you.
A force of 20 newton stretches a spring 1 meter. A 5 kg mass is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 10 times the instantaneous velocity. (a) Let x denote the downward displacement of the mass from its equilibrium position. [Note that x>0 when the mass is below the equilibrium position. ] Assume the mass is initially released from rest from a point 3 meters above the equilibrium position. Write the differential equation and the initial conditions for the function x(t)(b) Solve the initial value problem that you wrote above.(c) Find the exact time at which the mass passes through the equilibrium position for the first time heading downward. (Do not approximate.)(d) Find the exact time at which the mass reaches the lowest position. The "lowest position" means the largest value of x
4- Please I want solution of all sub-parts by typing. Many Thanks
2- A free vibrations test is run to determine the stiffness and damping properties of an elastic element. A 20 kg block is attached to the element. The block is displaced 1 cm and released. The resulting oscillations are monitored with the results shown in Figure (1). Determine k and c for this element. 0.01 0.008 0.006 0.004 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 0 0.06 0.12 0.18 Figure (1) 0.24 0.30 0.3

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