PRACTICE PROBLEM 9.13two minecarts are connected as shown below. Friction is negligible.If you know that:• Minecart 1 mass-8 kilograms• Mine cart 1 velocity = 3 m/s to the rightmm ₂KDifferential eq:*-[],=• Minecart 2 mass-4 kilograms• Minecart 2 velocity = 3 m/s to the left• Minecart 2 will stick to minecart 1 upon impact via the spring on minecart 2. This spring has aconstant (k) -8 N/mSolution:21(t)=wall• Minecart 2 is 10 meters away from the wall.• Time (t)=0 is when the mine carts collide and stick together.• x1 and x2 is the displacement of minecart 1 and 2 respectively from its original position at t-0Make a second order differential equations system that models the situation and find the solution to thesystem you make.10mx₂(t)

Given:Mass of the first object is Mass of the second object is Spring constant is .The initial…

PRACTICE PROBLEM 9.13 two minecarts are connected as shown below. Friction is negligible. If you know that: • Minecart 1 mass-8 kilograms • Mine cart 1 velocity = 3 m/s to the right Minecart 2 mass-4 kilograms Differential eq: *-[]• = MM K Solution: 2₁ (t) =_ • Minecart 2 velocity = 3 m/s to the left • Minecart 2 will stick to minecart 1 upon impact via the spring on minecart 2. This spring has a constant (k) -8 N/m • Minecart 2 is 10 meters away from the wall. • Time (t)=0 is when the mine carts collide and stick together. x1 and x2 is the displacement of minecart 1 and 2 respectively from its original position at t=0 Make a second order differential equations system that models the situation and find the solution to the system you make. wall. x₂(t) 10m

PRACTICE PROBLEM 9.13 two minecarts are connected as shown below. Friction is negligible. If you know that: • Minecart 1 mass-8 kilograms • Mine cart 1 velocity = 3 m/s to the right Minecart 2 mass-4 kilograms Differential eq: *-[]• = MM K Solution: 2₁ (t) =_ • Minecart 2 velocity = 3 m/s to the left • Minecart 2 will stick to minecart 1 upon impact via the spring on minecart 2. This spring has a constant (k) -8 N/m • Minecart 2 is 10 meters away from the wall. • Time (t)=0 is when the mine carts collide and stick together. x1 and x2 is the displacement of minecart 1 and 2 respectively from its original position at t=0 Make a second order differential equations system that models the situation and find the solution to the system you make. wall. x₂(t) 10m

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

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Question

PRACTICE PROBLEM 9.13
two minecarts are connected as shown below. Friction is negligible.
If you know that:
• Minecart 1 mass-8 kilograms
• Mine cart 1 velocity = 3 m/s to the right
mm ₂
K
Differential eq:
*-[],
=
• Minecart 2 mass-4 kilograms
• Minecart 2 velocity = 3 m/s to the left
• Minecart 2 will stick to minecart 1 upon impact via the spring on minecart 2. This spring has a
constant (k) -8 N/m
Solution:
21(t)=
wall
• Minecart 2 is 10 meters away from the wall.
• Time (t)=0 is when the mine carts collide and stick together.
• x1 and x2 is the displacement of minecart 1 and 2 respectively from its original position at t-0
Make a second order differential equations system that models the situation and find the solution to the
system you make.
10m
x₂(t)

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Step 1: Determine the second order differential equation system that models the situation and also solution.

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Step 2: Calculate the natural frequency.

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Step 3: Calculate the Differential equation in matrix form.

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Step 4: Calculate the Solution of the differential equation.

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