Solve the following ODE proble using Laplace. [Ignoring units for simplicity] The average electromagnetic railgun on a Gundam consists of a frictionless, open-to-the-environment, rail in which a projectile of mass m is imparted a force F from time t = 0 to time f=t₁. Before and after the bullet exits the railgun, it experiences the normal resistance due to its environment, i.e. Fr = ŋv(t), where v(t) is the instanteneous speed of the bullet. The one-dimensional trajectory of the bullet is then described by the differential equation my"(t) = FĐ(t)Đ(–t+h)−ny(t), with y(0) 0 = y'(0). We would like to use this to see if the Gundam can hit a moving target. Use the convolution theorem to solve to find the solution y(t) of the differential equation. What is the equation for y(t) fort > t₁? y(t) = [Hint: it should be a linear combiantion of two exponentials and a cosntant] Plot y(t) as a function of t for a fixed F.
Solve the following ODE proble using Laplace. [Ignoring units for simplicity] The average electromagnetic railgun on a Gundam consists of a frictionless, open-to-the-environment, rail in which a projectile of mass m is imparted a force F from time t = 0 to time f=t₁. Before and after the bullet exits the railgun, it experiences the normal resistance due to its environment, i.e. Fr = ŋv(t), where v(t) is the instanteneous speed of the bullet. The one-dimensional trajectory of the bullet is then described by the differential equation my"(t) = FĐ(t)Đ(–t+h)−ny(t), with y(0) 0 = y'(0). We would like to use this to see if the Gundam can hit a moving target. Use the convolution theorem to solve to find the solution y(t) of the differential equation. What is the equation for y(t) fort > t₁? y(t) = [Hint: it should be a linear combiantion of two exponentials and a cosntant] Plot y(t) as a function of t for a fixed F.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Solve the following ODE proble using Laplace.
[Ignoring units for simplicity]
The average electromagnetic railgun on a Gundam consists of a frictionless, open-to-the-environment, rail in which a projectile of mass m is imparted a
force F from time t = 0 to time f = ₁. Before and after the bullet exits the railgun, it experiences the normal resistance due to its environment, i.e.
FR = n(t), where v(t) is the instanteneous speed of the bullet. The one-dimensional trajectory of the bullet is then described by the differential
equation
my" (t) = Fə(t)=(−1+₁)-ny'(t),
with y(0)=0-3'(0). We would like to use this to see if the Gundam can hit a moving target.
Use the convolution theorem to solve to find the solution y(t) of the differential equation.
What is the equation for y(t) for t > t₁?
y(t) =
[Hint: it should be a linear combiantion of two exponentials and a cosntant]
Plot y(t) as a function of t for a fixed F.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37ebe49-731c-47f9-a49b-3a5f656faaa2%2F528f8b0a-6ad3-4b24-9fa8-c6305dbf9e1b%2Fffdmgj_processed.png&w=3840&q=75)
Transcribed Image Text:Solve the following ODE proble using Laplace.
[Ignoring units for simplicity]
The average electromagnetic railgun on a Gundam consists of a frictionless, open-to-the-environment, rail in which a projectile of mass m is imparted a
force F from time t = 0 to time f = ₁. Before and after the bullet exits the railgun, it experiences the normal resistance due to its environment, i.e.
FR = n(t), where v(t) is the instanteneous speed of the bullet. The one-dimensional trajectory of the bullet is then described by the differential
equation
my" (t) = Fə(t)=(−1+₁)-ny'(t),
with y(0)=0-3'(0). We would like to use this to see if the Gundam can hit a moving target.
Use the convolution theorem to solve to find the solution y(t) of the differential equation.
What is the equation for y(t) for t > t₁?
y(t) =
[Hint: it should be a linear combiantion of two exponentials and a cosntant]
Plot y(t) as a function of t for a fixed F.
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