A block with mass m slides without friction down an incline on a moving cart of mass 4m. Use Lagrange's equations to derive the two equations of motion for the system, using generalized coordinates q₁ = ₁, the distance from the moving cart to the wall relative to spring equilibrium, and 92 = 2, the distance from the sliding mass to the top of the cart along the incline relative to spring equilibrium. HINT: The velocity of the mass on the incline can be written as the sum of the velocity of the cart and the velocity of the mass relative to the cart. You should break that velocity down into x and y components to find the total speed.

A block with mass m slides without friction down an incline on a moving cart of mass 4m. Use Lagrange's equations to derive the two equations of motion for the system, using generalized coordinates q₁ = ₁, the distance from the moving cart to the wall relative to spring equilibrium, and 92 = 2, the distance from the sliding mass to the top of the cart along the incline relative to spring equilibrium. HINT: The velocity of the mass on the incline can be written as the sum of the velocity of the cart and the velocity of the mass relative to the cart. You should break that velocity down into x and y components to find the total speed.

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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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

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A block with mass m slides without friction down an incline on a moving cart of mass 4m. Use
Lagrange's equations to derive the two equations of motion for the system, using generalized
coordinates 91 = ₁, the distance from the moving cart to the wall relative to spring equilibrium, and
92 = €2, the distance from the sliding mass to the top of the cart along the incline relative to spring
equilibrium.
HINT: The velocity of the mass on the incline can be written as the sum of the velocity of the cart and
the velocity of the mass relative to the cart. You should break that velocity down into x and y
components to find the total speed.
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