Mechanical system consists of: body 1 of mass m m: body 3 two-stage disk of mass m36m. radii r and R=2r, and wwww radius of inertia = toward horizontal axes passing through its center: both bodies 4- equal horizontal springs cach of coe- licient of clasticity c. An ideal cord 2 connects body 1 and body 3. Disk 3 moves by its small drum on a fixed horizontal plane without sliding. At the initial moment system is turned out of its equilibrium by small shifting of magnitude x of the body 1 in the x direction (according to the ligure) and released with initial velocity of magnitude v. Assuming the system makes small oscillations around its equilibrium, neglecting resistance forces, and m.r.c are positive constants, find: a) kinetic energy of the system; b) total power of the forces acting upon the system; c) differential equation of the system motion (using the body I motion at x direction): d) the law of the system motion (using the body 1 motion at x direction).

Mechanical system consists of: body 1 of mass m m: body 3 two-stage disk of mass m36m. radii r and R=2r, and wwww radius of inertia = toward horizontal axes passing through its center: both bodies 4- equal horizontal springs cach of coe- licient of clasticity c. An ideal cord 2 connects body 1 and body 3. Disk 3 moves by its small drum on a fixed horizontal plane without sliding. At the initial moment system is turned out of its equilibrium by small shifting of magnitude x of the body 1 in the x direction (according to the ligure) and released with initial velocity of magnitude v. Assuming the system makes small oscillations around its equilibrium, neglecting resistance forces, and m.r.c are positive constants, find: a) kinetic energy of the system; b) total power of the forces acting upon the system; c) differential equation of the system motion (using the body I motion at x direction): d) the law of the system motion (using the body 1 motion at x direction).

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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Concept explainers

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,

Question

PROBLEM 3
Mechanical system consists of: body 1 of mass m=m; body 3
(MA
- two-stage disk of mass m 6m, radii r and R=2r, and
R.
3.
radius of inertia i= toward horizontal axes passing through
4.
its center: both bodies 4- equal horizontal springs cach of coe-
licient of clasticity c. An ideal cord 2 connects body 1 and
body 3. Disk 3 moves by its small drum on a fixed horizontal
plane without sliding. At the initial moment system is turned
out of its equilibrium by small shifting of magnitude x of the body 1 in the x direction (according to the
figure) and released with initial velocity of magnitude v. Assuming the system makes small oscillations
around its equilibrium, neglecting resistance forces, and m,r.c are positive constants, find:
a) kinetic energy of the system%3B
b) total power of the forces acting upon the system;
c) differential equation of the system motion (using the body I motion at x direction):
d) the law of the system motion (using the body 1 motion at x dircction).
ww.

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