Question

So I have no idea how to set up #1. I'm pretty sure I can find the particular solution once I know the equation, but I would just love some help of that as well.

I included this second page as a formality, feel free not to use the website.
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Introduction: An Army cannon is designed so that when a shell is fired from it, the carriage that the gun tube assembly sits on remains stationary, while the gun tube assembly slides in recoil, as shown in the diagram below. Gun tube assembly Breech Recoil Can tube lock spring Damping poestive direction natve direction When a shell is fired, two components between the gun tube assembly and the carriage absorb the recoil: a damping mechanism and a recoil spring. The recoil spring has the additional function of pushing the gun tube assembly back to the starting position, so that another shell can be loaded and fired. The gun tube assembly has a mass of 1,600 kilograms. The recoil spring has a spring constant of 20,000 Newtons per meter The damping mechanism exerts a force, in Newtons, numerically equal to9 instantaneous velocity, in meters per second, of the gun tube assembly. ,500 times the Problem #1 [24 points total] For this problem, assume that, when the cannon is fired, the gun tube assembly is pushed to the rear with an initial instantaneous velocity of 5 meters per second (to the right in the diagram). Assume that motion of the gun tube assembly to the right in the diagram is negative. Model this system as an initial-value differential equation problem, where 0) and 1. r is the displacement of the gun tube assembly from the starting position (x 0) and r is time in seconds. Type or write "The initial-value problem is", followed by your answer. (5 points) Use a computer program or computing algebra system (CAS) calculator to find the particular solution that gives the displacement of the gun tube assembly with respect to time. 2. Type or write "The particular solution for the problem is", followed by your answer. (4 points) Suggested Internet site: https://www.wolframalpha.com/examples/mathematics/differential-equations/ NOTES on entering formulas in this program: a. To solve an initial-value system of differential equations, in the command line, b. You do NOT need to use an asterisk to represent multiplication operations; c. You must use a carat " to raise an expression to a power. d. You can use "e" to represent the natural base e. e. You can use either differential or prime notation to enter a derivative expression. enter the equations and conditions, separated by commas, and click the “-" button on the right side of the command line. however, you may do so if you wish. For example, to enter "2x", type "2x". For example, to enter" 2x ”, type "21x". For example, to enter ", type "ex2x". For example, you can express the derivative of y with respect to x as either "dy/dx" or "y".

Answer 1

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