6.25. A 30,000-kg locomotive is coupled to a fully loaded 20,000-kg boxcar and moving at 6.5 m/s. The assembly is coupled to a stationary and empty 5,000-kg cattle car. The stiffness of each coupling is 5.7 × 10° N/m. (a) What are the natural frequencies of the three-car assembly? (b) Mathematically describe the motion of the cattle car after coupling.

6.25. A 30,000-kg locomotive is coupled to a fully loaded 20,000-kg boxcar and moving at 6.5 m/s. The assembly is coupled to a stationary and empty 5,000-kg cattle car. The stiffness of each coupling is 5.7 × 10° N/m. (a) What are the natural frequencies of the three-car assembly? (b) Mathematically describe the motion of the cattle car after coupling.

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

Similar questions

Mechanical Vibration Problem
Vibration
A block of mass m = 400 g, is attached to a horizontal spring and set in simple harmonic motion as shown. At what point(s) in the motion is the velocity of the block at its maximum? ww X = -A O a. x = 0, and x = -A O b. x=0, x= -A, and x = -A O e. O c. O d. x = 0 x = -A, and x = +A . x = 0, and x = +A m x = 0 X = +A
Two identical circular cylinders of radius r and mass m each, are connected by a spring, as shown below. Derive the equations of motion using Lagrange's equations. Please indicate the lowest natural vibration frequency. (1 =mr?) k m
Problem 5.1 A rotational spring-mass system is shown to the right. The slender rigid bar has a mass of 18 kg and a length of { = 1.5 m. The springs have stiffness k = 360 N/m. The bar has a displacement of –0.06 rad and a speed of –1.1 rad/s when a harmonic moment M (t) = (80 N·m)cos 16t is applied. Find the response of the system. Assume small displacements. You will need to solve the differential equation because the results from lecture and in the book are for M(t) = M sin wt, not M (t) = Mo cos wt. You do not have to derive the homogeneous solution from scratch; you may use equations from Module 3, but the coefficients will be different. k - 3 Мо cos ot Answer: 0 (t) = {0.0540 cos 10t – 0.110 sin 10t 0.114 cos 16t} rad k
As shown in the figure, a homogeneous rod with a length L = 1 (m) and mass m = 0.2 (kg) is fixed so that it can rotate in the middle. Two springs with constant k = 30 (N/m) are connected at both ends of the rod. The other ends of the springs are fixed and the springs are unstretched. The rod is rotated as 0 « from its equilibrium position and released. What is the angular frequency of the rod in (rad/s)? g = 10 (m/s²) k т, L k A) 10 В) 12 С) 15 D) 30 E) 60
find the mass of the automobile by treating it as an undamped single-degree-of-freedom system?(Need handwritten solution only please otherwise downvote)
A three-blade wind turbine used for research is supported on a shaft so that it is free to rotate about O. One technique to determine the centroidal mass moment of inertia of an object is to place a known weight at a known distance from the axis of rotation and to measure the frequency of oscillations after releasing it from rest with a small initial angle. In this case, a weight of Wadd = 50 lb is attached to one of the blades at a distance R = 20 ft from the axis of rotation. Knowing that when the blade with the added weight is displaced slightly from the vertical axis, and the system is found to have a period of 7.6 s, determine the centroidal mass moment of inertia of the three-blade rotor.
1. A machine component of mass 0.77 kg moves with SHM in a straight line and completes 175 oscillations per minute. Find the accelerating force when the component is 50 mm from mid-travel.
1. An undamped spring-mass system is shown below. (a) Starting from the equations of motion, find the natural frequencies of the system. if m₁ = m, m₂ = 2m, k₁=k, and k₂ = 2k. (b) Find the natural frequencies and mode shapes (i.e. modal vectors) of the system if m₁ = m₂ = 1 kg, k₁ = 2000 N/m, and k₂ = 6000 N/m. (c) Given the properties in (b), determine the response of the system x₁(t) and x₂(t) if the initial conditions are x₁(0) = 0.2 m, ₁ (0) = x₂(0) = 0, and ₂(0) = 5 m/s. Base k₁ k₂ reelle m₁ m₂ x₁ (t) x₂ (1) Undamped 2 DOF spring-mass system.
Q4. An air-conditioning chiller unit weighing 5.0kg is to be supported by four air springs. Design the air springs such that the natural frequency of vibration of the unit liesbetween 5 rad/s and 10 rad/s. Q5. A heavy machine weighing 9.81kN is being lowered vertically down by a winch at a uniform velocity of 2 m/s. The steel cable supporting the machine has a diameter of 0.01 m. The winch is suddenly stopped when the steel cable's length is 20 m. Find the period and amplitude of the ensuing vibration of the machine when Young's Modulus of steel cable is 2.07*10¹1 N/m².
* F2 # 3 E Problem 4. EOM Derivation Derive the equation of motion for the following system: We want to measure the spin rate w of the rotating shaft of a turbine. To do it we push a small mass m against the end of the shaft. The shaft makes friction contact with the drag cup mounted on the mass. The frictional torque is b (w). Assume that the rotational spring torque is ke and that the moment of inertia of mass m is J. J Rotating Shaft F3 @ $ 4 R b J, m Drag Cup F4 Q Search % 5 F5 T 0 Wall * A 6 F6 Y 2 * F7 & 7 PrtScn U F8 4 8 Home 6. F9 9 End F10 Po 0