t. Design the following application caseThe mechanical vibration system is shown in Figure (a). When a step input with3N amplitude is subjected to this system, the movement rule of the mass m isshown in Figure (b). Evaluate the values of mass m, damping constant c andspring constant k.m(a)F-3NXX1.0x(1)(cm)02(b)M,-0.095Ⓒ

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Answered: t. Design the following application…

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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(2) Please write out the Equation of Movements of the following system using matrix. (Figure 2) 1 Note: Lagrange's approach is recommended. „P₂(t) ks ww P₁(t) k₁ wwm, www k₂ m₂ k6 www P3(t) k₁ k3 www m3 www Figure 2: N Degree Vibration System
t. Design the following application case m is The mechanical vibration system is shown in Figure (a). When a step input with shown in Figure (b). Evaluate the values of mass m, damping constant c and spring constant k. B (a) yu P=2N X(t)/cm4 0.1095 0.1 0 2 (b) 3 4
1. Suppose you are riding your bicycle on a bumpy road having a surface profile that varies harmonically with +/- 6 cm undulations. The distance between consecutive peaks of these undulations is 2 m. When you sit on the seat of your bike for your casual ride, the springs deflect 5 cm. When you are seated, the damper under the seat provides an equivalent linear viscous damping of 10% of the critical damping. A simple representation of your ride on the "never-ending" rough road is shown below. (a) If you are riding your bicycle at a horizontal speed of 2.5 m/sec, how much bumping up and down will you experience? (b) Next day, you are carrying a backpack which increases your on-seat weight by 20%. Assuming that you are still able to ride with same speed, will this "loaded" ride be more or less comfortable than your previous, "no backpack" ride? M k/23 k/2 6 cm 2 m
A mechanical dynamic system is having two degrees of freedom as shown in figure 2. The given parameters are mass is 3 Kg, damping factors b;= 5 N-s/m, b2= 2 N-s/m and b3= 1 N- s/m, the spring constants k1= 3 N/m, k2= 6 N/m and k3= 2 N/m. Base on this diagram, determine the following. i. Draw and label complete Free Body Diagram of the network. ii. The differential equations representing the system. X2(s) F(s) iii. The transfer function iv. What is the effect connecting springs and damper in this configuratior. f(t) m2 b, b, b, Figure 2
My question and answer is in the image. Can you please check my work? A 2 kg mass is attached to a spring with spring constant 50 N/m. The mass is driven by an external force equal tof(t) = 2 sin(5t). The mass is initially released from rest from a point 1 m below the equilibrium position. (Use theconvention that displacements measured below the equilibrium position are positive.)(a) Write the initial-value problem which describes the position of the mass. 2y"+50y=2cos(5t) (b) Find the solution to your initial-value problem from part (a). (1+(1/2)tcos(t))cos(5t)-(1/2)tcos(t) (c) Circle the letter of the graph below that could correspond to the solution. B (d) What is the name for the phenomena this system displays? Resonance
The slender bar of Figure 3.9(a) has a mass of 31 kg and a length of 2.6 m. A 50 N force is statically applied to the bar at P then removed. The ensuing oscillations of Pare moni- tored, and the acceleration data is shown in Figure 3.9(b) where the time scale is calibrated but the acceleration scale is not. (a) Use the data to find the spring stiffness k and the damping cocfficient c. (b) Calibrate the acceleration scale.
A 0.1kg object oscillator as a simle harmonic motion along the x _axis with a frequency f=3.18 hz at a position x1,the object has a kinetic energy 0.7j and a potential energy 0.3j,the amplitude of oscillation A is:
A body of mass 100 kKg is suspended by a spring of stifness of 30KN/m and a dashpot of damping constant 1000 N.s/m. Vibration is excited by harmonic force ft)=80 cos (67tt) 1- Write the equation of motion of the system using Lagrange's equation. 2- Find the natural frequency and the driving frequency. 3- Write the complete solution of the vibrating system.
i, Consider the following 1-DOF system, where k :0-3 kg, calculate the natural frequency in rad/s and Hz. Also find the period of scillations and the maximum displacement if the spring isinitially displaced 10 am with no initial velocity. 857.8 N/m and m = 49.2 x
x(t) 0000000000 m kea F Vibration model Fo Fo F(t) T 2T t (sec) The vibration model is subjected to the force shown in the figure. Find the response of the system for time t>2T
A simple pendulum whose string measures 1 = 2 m and whose mass is 5 kg is at rest in its position of equilibrium and is subjected to a harmonic forcing of intensity F₁ = 2 N and frequency w rad/s. find: a) The frequency @ for which the system is in resonance. b) Make a graph of angular position v/s time where the amplitude and period of the system if the frequency w is equal to twice the resonant frequency.
Given the vibrating system below: K4 Y(t) =Ysin30t where for = 30 and Y=20mm Find the following K1 K2 m C3 H C2 C1 C5 C4 1. Frequency Ratio 2. Displacement Transmissibility Ratio 3. Absolute displacement of the mass 4. Type of Damping 5. Equation of motion x(t). Assume Initial conditions for displacement and velocity 6. Graph 2 cycles of the vibrating system. You can use third party app for this. M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2=40 Ns/m C3= 35Ns/m C4= 15 Ns/m C5= 10 Ns/m

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