Mechanical system consists of: body 1 of mass m=m; body 3 – two-stage disk of mass m3=4m, radii r and R 3 R=2r, and radius of inertia iz= toward horizontal 4 axes passing through its center; both bodies 4 – equal horizontal springs each of coefficient of elasticity 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 xo of the body 1 in the x direction (according to the figure) and released with initial velocity 4 of magnitude Vo. 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 1 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.
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Mechanical system consists of: body 1 of mass m¡=m;
body 3 – two-stage disk of mass m3=4m, radii r and
2.
R
R=2r, and radius of inertia iz= toward horizontal
4
axes passing through its center; both bodies 4 – equal
horizontal springs each of coefficient of elasticity 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 xo of the body 1 in the x direction (according to the figure) and released with initial velocity
4
of magnitude vo· 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 1 motion at x direction);
d) the law of the system motion (using the body 1 motion at x direction).
3,
Transcribed Image Text:Mechanical system consists of: body 1 of mass m¡=m; body 3 – two-stage disk of mass m3=4m, radii r and 2. R R=2r, and radius of inertia iz= toward horizontal 4 axes passing through its center; both bodies 4 – equal horizontal springs each of coefficient of elasticity 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 xo of the body 1 in the x direction (according to the figure) and released with initial velocity 4 of magnitude vo· 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 1 motion at x direction); d) the law of the system motion (using the body 1 motion at x direction). 3,
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In a) why you wrote ( m + 5m) , where that 5m came? You have m1 = m and m3 = 4m in the problem. So it must be (m + 4m), but istead 4m you wrote 5m, why?

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