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 t = t₁. 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) = F÷(t)¤(−t+t₁)-ny' (t), with y(0) = 0 = y'(0). We would like to use this to see if the Gundam can hit a moving target. a) Apply the Lapalce transform on both sides and obtain the corresponding equation for L[y(t)](s). Fill in the gaps below to give your answer, i.e., Ly(t)](s) = F(1-e-¹²) P() where P(s) - Xs+
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 t = t₁. 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) = F÷(t)¤(−t+t₁)-ny' (t), with y(0) = 0 = y'(0). We would like to use this to see if the Gundam can hit a moving target. a) Apply the Lapalce transform on both sides and obtain the corresponding equation for L[y(t)](s). Fill in the gaps below to give your answer, i.e., Ly(t)](s) = F(1-e-¹²) P() where P(s) - Xs+
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 t = t₁. 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) = F(t) (-t+t₁)-ny' (t),
with y(0) = 0 = y'(0). We would like to use this to see if the Gundam can hit a moving target.
a)
Apply the Lapalce transform on both sides and obtain the corresponding equation for Lly(t)](s). Fill in the gaps below to give your answer, i.e.,
F(1-¹)
Ly(t)](s) =
P(s)
where P(s):
X8³+
X8² +
X8+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37ebe49-731c-47f9-a49b-3a5f656faaa2%2Ff038aaca-d324-482e-bd94-d614faa6c27a%2Fpkwa1dl_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 t = t₁. 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) = F(t) (-t+t₁)-ny' (t),
with y(0) = 0 = y'(0). We would like to use this to see if the Gundam can hit a moving target.
a)
Apply the Lapalce transform on both sides and obtain the corresponding equation for Lly(t)](s). Fill in the gaps below to give your answer, i.e.,
F(1-¹)
Ly(t)](s) =
P(s)
where P(s):
X8³+
X8² +
X8+
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