A box with a mass of 3m is on frictionless ground, attached to a wall (on the left-side of the box) by a spring with constant k. Inside the box (on the frictionless floor of the box), is a block of mass m. The block is also attached to the left-side of the box (but inside it), by a second spring, with a spring constant 2k/5. 1) What are the F = ma equations for the box and the block? (Remember how the motion of each, affects each other) 2) What are the matrices K and M for the system? 3) What are the normal frequencies of the system? 4) Describe the motion of the masses. In phase? Out of phase? Does one mass oscillate with a higher amplitude than the other?
A box with a mass of 3m is on frictionless ground, attached to a wall (on the left-side of the box) by a spring with constant k. Inside the box (on the frictionless floor of the box), is a block of mass m. The block is also attached to the left-side of the box (but inside it), by a second spring, with a spring constant 2k/5. 1) What are the F = ma equations for the box and the block? (Remember how the motion of each, affects each other) 2) What are the matrices K and M for the system? 3) What are the normal frequencies of the system? 4) Describe the motion of the masses. In phase? Out of phase? Does one mass oscillate with a higher amplitude than the other?
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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A box with a mass of 3m is on frictionless ground, attached to a wall (on the left-side of the box) by a spring with constant k. Inside the box (on the frictionless floor of the box), is a block of mass m. The block is also attached to the left-side of the box (but inside it), by a second spring, with a spring constant 2k/5.
1) What are the F = ma equations for the box and the block? (Remember how the motion of each, affects each other)
2) What are the matrices K and M for the system?
3) What are the normal frequencies of the system?
4) Describe the motion of the masses. In phase? Out of phase? Does one mass oscillate with a higher amplitude than the other?
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