question 2A mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with an angular velocity ,, as shown in the figure below. The rim of the pulley is attached to a spring (with constant 7). Assume small oscillations so that the spring remains essentially horizontal and neglect friction so that the conservation of energy of the system yields: 1 2 !91 + 1 2 6,1 + 1 2 7;1 − !); = =, ?ℎABA , = 9 5 , = = CDE&/, ; = FG&H'5CA!AE/ IBD! AJ(G'GKBG(! Find the natural circular frequency of the system in terms of !, 5, 7,6, and ). 1) A building consists of two floors. The first floor is attached rigidly to the ground, and the secondfloor is of mass m = 1000 slugs (fps units) and weighs 16 tons (32,000 lb). The elastic frame ofthe building behaves as a spring that resists horizontal displacements of the second floor; itrequires a horizontal force of 5 tons to displace the second floor a distance of 1 ft. Assume that inan earthquake the ground oscillates horizontally with amplitude A, and circular frequency w,resulting in an external horizontal force F(t)What is the natural frequency (in hertz) of oscillations of the second floor?b. If the ground undergoes one oscillation every 2.25 s with an amplitude of 3 in, what is theamplitude of the resulting forced oscillations of the second floor?mA,w²sin(wt) on the second floor.а.2) A mass m hangs on the end of a cord around a pulley of radius a and moment of inertia I, rotatingwith an angular velocity w, as shown in the figure below. The rim of the pulley is attached to aspring (with constanthorizontal and neglect friction so that the conservation of energy of the system yields:Assume small oscillations so that the spring remains essentially11z mv² +,lw? +,kx² – mgx = C,where w =-,C =const,x =displacement from equilibriumaFind the natural circular frequency of the system in terms of m, a, k, 1, and g.wwIaミ

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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 mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with an angular velocity ,, as shown in the figure below. The rim of the pulley is attached to a spring (with constant 7). Assume small oscillations so that the spring remains essentially horizontal and neglect friction so that the conservation of energy of the system yields: 1 2 !91 + 1 2 6,1 + 1 2 7;1 − !); = =, ?ℎABA , = 9 5 , = = CDE&/, ; = FG&H'5CA!AE/ IBD! AJ(G'GKBG(! Find the natural circular frequency of the system in terms of !, 5, 7,6, and ).

1) A building consists of two floors. The first floor is attached rigidly to the ground, and the second
floor is of mass m = 1000 slugs (fps units) and weighs 16 tons (32,000 lb). The elastic frame of
the building behaves as a spring that resists horizontal displacements of the second floor; it
requires a horizontal force of 5 tons to displace the second floor a distance of 1 ft. Assume that in
an earthquake the ground oscillates horizontally with amplitude A, and circular frequency w,
resulting in an external horizontal force F(t)
What is the natural frequency (in hertz) of oscillations of the second floor?
b. If the ground undergoes one oscillation every 2.25 s with an amplitude of 3 in, what is the
amplitude of the resulting forced oscillations of the second floor?
mA,w²sin(wt) on the second floor.
а.
2) A mass m hangs on the end of a cord around a pulley of radius a and moment of inertia I, rotating
with an angular velocity w, as shown in the figure below. The rim of the pulley is attached to a
spring (with constant
horizontal and neglect friction so that the conservation of energy of the system yields:
Assume small oscillations so that the spring remains essentially
1
1
z mv² +,lw? +,kx² – mgx = C,
where w =-,C =
const,x =
displacement from equilibrium
a
Find the natural circular frequency of the system in terms of m, a, k, 1, and g.
ww
I
a
ミ

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