4. Here is an equation for a spring-mass system: r" + 4x' + 5x = 0. (a) What are the interpretations of the " 4 "and the "5 " ? (b) Find the general solution. (c) Give a rough sketch of the solution to the equation using the initial values r(0) -1, a (0) = -1. (You do not need to solve the IVP to do this, so do not solve the IVP.)

4. Here is an equation for a spring-mass system: r" + 4x' + 5x = 0. (a) What are the interpretations of the " 4 "and the "5 " ? (b) Find the general solution. (c) Give a rough sketch of the solution to the equation using the initial values r(0) -1, a (0) = -1. (You do not need to solve the IVP to do this, so do not solve the IVP.)

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.8.11P: A bumper for a mine car is constructed with a spring of stiffness k = 1120 lb/in. (see figure). If a...

See similar textbooks

Similar questions

A small lab scale has a rigid L-shaped frame ABC consisting of a horizontal aim AB (length b = 30 cm) and a vertical arm BC (length c = 20 cm) pivoted at point B. The pivot is attached to the outer frame BCD that stands on a laboratory bench. The position of the pointer at C is controlled by two parallel springs, each having a spring constant k = 3650 N/m. that are attached to a threaded rod. The pitch of the threads is p = 1.5 mm. If the weight is 65 N. how many revolutions of the nut are required to bring the pointer back to the mark?
A bumper for a mine car is constructed with a spring of stiffness k = 1120 lb/in. (see figure). If a car weighing 3450 lb is traveling at velocity v = 7 mph when it strikes the spring, what is the maximum shortening of the spring?
5.2 In a compound helical spring, the inner spring is concentric with the outer spring, but is 9 mm shorter. The outer spring has ten coils of mean diameter 24 mm, and the wire diameter is 3 mm. Find the stiffness of the inner spring if an axial load of 150 N causes the outer spring to compress 18 mm. If the mean coil diameter for the inner spring is 15.94 mm, find the wire diameter of the inner spring when it has eight coils. Both the springs are made of the same material having G = 77 GPa.
Figure below shows a mass-spring model of the type used to design packaging systems and vehicle suspensions, for example. The springs exert a force that is proportional to their compression, and the proportionality constant is the spring constant k. The two side springs provide additional resistance if the weight W is too heavy for the center spring. When the weight W is gently placed, it moves through a distance x before coming to rest. From statics, the weight force must balance the spring forces at this new position. (if x=d) These relations can be used to generate the plot of x versus W. (a) The following values are given: k1=104 N/m; k2 = 1.5 *104 N/m; d =0.1 m. Create a function that computes the distance x, using the input parameter W; Then, test your function for the following two cases, using the values: W=500 N W=2000 N. (b) Create another script and use your function to plot x versus W for 0 < W < 3000 N for the values of k1, k2, and d given in part a.
Find the number of active coils of a No. 10 wire Helical Spring index of 7, steady load with spring rate of 46.5 lb/in. maximum allowable stress is 70 ksi. The stiffness of a spring is 98 N/mm of axial compression. Find the Joules of work to increase the compression from 60 mm to 90 mm.
Under some circumstances, when two parallel springswith constants k1 and k2 support a single mass, theeffective spring constant of the system is given byk 4k1k2/(k1 + k2). A mass weighing 20 pounds stretchesone spring 6 inches and another spring 2 inches. Thesprings are first attached to a common rigid supportand then to a metal plate. As the figure illustrates(see image), the mass is attached to the center of the plate in the distributiondouble spring. Determine the constant of theeffective spring for this system. find the equationof motion if the mass is initially released fromequilibrium position with downward speed of2 ft/sec.
From the following diagram find with k1=20N/m, k2=30 N/m, k3=25 N/m, k4=35 N/m, k5=50N/m and k6=60N/m, m=10kg A) the equivalent spring B) the displacement C) the work performed
5.1 Determine the spring constant of the spring arrangement if all springs have the same spring constant. 5.2 In a compound helical spring, the inner spring is concentric with the outer spring, but is 9 mm shorter. The outer spring has ten coils of mean diameter 24 mm, and the wire diameter is 3 mm. Find the stiffness of the inner spring if an axial load of 150 N causes the outer spring to compress 18 mm. If the mean coil diameter for the inner spring is 15.94 mm, find the wire diameter of the inner spring when it has eight coils. Both the springs are made of the same material having G = 77 GPa.
A helical spring is made of 10 m diameter steel wire wound on a 100 mm diameter mandrel. If there are 10 active coils what is spring constant Take: C= 100 GPA What force must be applied to the spring to elongate it by 50 mm?
Figure 1.29 shows the suspension system of a freight truck with a parallel-spring arrangement. Find the equivalent spring constant of the suspension if each of the three helical springs is made of steel with a shear modulus G = 100 GPaand has 10 effective turns, mean coil diameter D = 50 cm, and wire diameter d = 5 cm
Problem 3: A helical spring is designed to have a stiffness of 500 N/m. The spring has a wire diameter of 5 mm and an outer diameter of 30 mm. Determine the number of coils required for the spring if the spring index is 6. Problem 4: A helical spring is compressed by a force of 100 N, resulting in a compression length of 20 cm. The spring has a wire diameter of 3 mm and a mean coil diameter of 15 cm. Determine the spring constant (stiffness) of the spring.
A closed-coil helical spring is to have stiffness of 900 N/m in compression with a maximum load of 45 N and a maximum shearing stress of 120 N/mm2.The length of the spring is 45 mm. find the wire diameter, mean coil radius and the number of coils. Take C= 40000 N/mm2