Homework 5

Introduction: provides general background about the suspension of motorcycle system of , its applications, and its components.

Please show your complete solution and correct answer to this problem. ASAP! Thank youuuu!

Response using Laplace transformation.

Q5: Find the equation of motion, natural frequency @ critical damping coefficient C., damping ratio , logarithmic decrement &, and damped frequency @ for the system shown in Fig. (5). Figure (5) IT TE X m=10kg C =500 N.s/m K-1000 N/m wwwww Pulley. Jo-1 kg.m²

Need only 3 to 5

I need part b (iv and v)

Mass: 10 kg Can move up and down only k: 600000 N/m Fixed a) Find the 1“ 5 natural frequencies for above system K 600,000 m 10 f = -=38.9848hz b) If a force F = 200sin50t is applied at the top of the system, find the time response of the lowest point of the mass. Assume damping 6% of critical damping. c) For case b, do harmonic analysis and find the response of the lowest point with frequency for 0-100 hz. Can you solve only part B and part C.

5- Please I want solution of all sub-parts by typing. Many Thanks

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

3. Consider the following system described below (parameters and inputs are in SI units): Im = 0.4 R = 0.18 k=30 b = 0.2 M m = 6 b=20 www Im T(t) = 2 R Mr Bammy Note: b is the damping coefficient between the mass and the ground (it is shown as c in the diagram, but we will use b). Complete the following: a) Find an equation of motion for the simplified equivalent mass system. Assume that the shaft between the inertias is rigid. b) Find the equations of motion in state variable form for this system. You should end up with 2 state variable equations. c) Numerically solve for the state variables and plot each state variable versus time. Assume, that the mass is initially displaced a distance of 0.1 in the positive direction and the mass velocity is initially zero. Also plot the spring force and damping force. d) This system is required to have a maximum displacement overshoot that is less than 15% of the steady state value to avoid the rack impacting another portion of the machine.…

Mass 15 kg. C=150 Ns/m, k = 200 N/m, a=0.5m, b = 0.75 m. Find: 1. Static equilibrium condition 2. Equation of motion of total resultant system 3. Natural frequency and damping ratio 4. Is system underdamped or overdamped? 5. What is equation to find transient response of this system? Just write equation. Do not find coefficients. 6. What is required value of mass m to make this system critically damped? QA b m B H

engineering vibration course

Sub- Mechanical vibrations

part b only please

Question is image. Only part ii) ?

I was not able to solve part d completely. Kindly help. Thank You.

Find the motion of the system in the figure below with mass 0.25 kg, no damping, spring constant 1 kg/sec², and driving force 120 cos(0.5t) - 56 sin(1.5t) nt, assuming zero initial displacement and velocity. For what frequency of the driving force would you get resonance? y(t) = = m Spring Mass Dashpot Mass-spring system Resonance for the frequency:

An engine valve assembly depicted is figure; where k = 857.8 N/m; c =7.8 kg/s, and m =0.0492 kg, calculate the natural frequency and damped frequency in rad/sec and Hz. What critical damping value, damping ratio and what damping * ?case is this system pivot rocker arm m cylinder head valve spring k combustion chamber pressure ww

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.

Problem 2. For the single-degree-of-freedom mechanical system shown in the figure, the bar has mass m and length l (so that Io spring is unstretched when 0 = 0: ml² 피). If the %3D k a) find the linearized governing equations of motion for small 0; (т,1) b) find the natural frequency, damping ration, and damped natural frequency of oscillation for the free response; Neglect gravity.

Figure 1 shows a system comprising a bar with mass m-12 kg and the length of the bar L=2 m, two springs with stiffness kt=1000 N-m/rad and k = 2000 N/m, one damper with damping coefficient c=50 N-s/m and two additive masses at the end of the bar, where each mass (M) is equal to 50 kg. The rotation about the hinge A, measured with respect to the static equilibrium position of the system is 0 (t). The system is excited by force (F) so find the state space representation of the system if the output y=ġ(t).

Mechanical Vibration Question is image A 100-kg tumbler produces a harmonic force of magnitude 5000 N. The stiffness coefficient of the support is 10×10^4N/m and damping coefficient ζ=0.2 If the maximum deflection is to be less than 0.06m find the operating frequency range?

Question (2). The following system has a block of a mass m = xykg(from your registration mUrnber), stiffness k= 12000 N/m, damping coefficient c = xy• 10 kg/s, base motion y(t)= 0.01 sin(3t), calculate the following: %3D 1 Natural frequency. 2 Base frequency. 3. Steady-state part of the response X(t) k y(1) base wW

For small positive damping, c, in the sinusoidally forced mass-spring system ma" + ca' + ka = Ggcos (wt) there is a value of the forcing frequency w for which the amplitude of the response is greatest - a resonance peak. very light darmping moderate damping very heavy darmping forcing frequency, w Derive a formula for the location of the peak in terms of the parameters in the differential equation (m, c, k; Go). So the location of the peak depends on the damping . Where does the peak move to as the damping constant c is reduced to zero? Does the above frequency have a name? amplitude of response

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. J6+ (kde) ds. C 0000 m

Given the vibrating system below: K4 Y(t) =Ysin30t where fos = 30 and Y=20mm Find the following K3 K1 K2 1. Frequency Ratio 2. Displacement Transmissibility Ratio 3. Absolute displacement of the mass m C3 C2 C1 C5 C4 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

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. J6+ (kdo) de. C 0000 m

Consider an underdamped mass spring system with mass m = 1 kg spring constant k = 8 N/m, and damping coefficient, stretched past equilibrium by 1 m and released with an initial velocity of 0 m/s. N.S a = 4 m www. Equilibrium Position (a) Write the solution of the initial value problem. x(t) = (b) Identify the pseudo-frequency. Find the circular frequency if damping is removed. m N s m (c) Determine the first time in seconds in which the mass returns to equilibrium position after being set in motion. (Round your answer to two decimal places.)

Consider a SDOF system having a mass m = 30 kN s2 /m, damping c = 50 kNs/m and stiffness k = 4000 kN/m. Determine natural frequency, damping ratio and critical damping. For x(0) = 0.02 m, and x . (0) = 0.1 m/s. Find the solution of the equation of motion. Hence, plot inertia, damping and spring force vs time for free vibration.

PROBLEM #3:- The mass of a spring.mass system vibrates on a dry surface inclined at 30 degrees to the horizontal as shown in problem 2. Find the system response for dry friction case, for the data m = 20 kg, k = 1,000 Nm, u=0.1, xo = 0.1 m