A mass weighing 20 Ib. stretches one spring 5 times as much as it stretches a second spring. The springs are attached to a common rigid support, and the mass is attached in the double- spring configuration, as shown in the figure. The 20-lb mass stretches the entire System by 2 inches, and after the System is set in motion att = 0, it is known that t = mv3/16 s, the spring is fully compressed to a distance of v3/12 ft from the equilibrium point. | 20 lb A-Determine the value of the effective total constant B-Determine the values of the constants k_1 and k_2 C-Propose a difference equation and the conditions that allow finding the equation of motion of the mass if it is initially released from the equilibrium position with an initial non-zero velocity lelllllll

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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In some circumstances when two parallel springs, with constants k, and k2, support a single
mass, the effective spring constant of the System k is expressed as:
4k k2
k =
k1 + kz
A mass weighing 20 Ib. stretches one spring 5 times as much as it stretches a second spring.
The springs are attached to a common rigid support, and the mass is attached in the double-
spring configuration, as shown in the figure. The 20-lb mass stretches the entire System by 2
inches, and after the System is set in motion at t = 0, it is known that t = nV3/16 s, the
spring is fully compressed to a distance of v3/12 ft from the equilibrium point.
k
20 lb
A-Determine the value of the effective total constant
B-Determine the values of the constants k_1 and k_2
C-Propose a difference equation and the conditions that allow finding the equation of motion
of the mass if it is initially released from the equilibrium position with an initial non-zero
velocity
D-Find the equation of motion of mass
E-Determine the initial speed and direction
Transcribed Image Text:In some circumstances when two parallel springs, with constants k, and k2, support a single mass, the effective spring constant of the System k is expressed as: 4k k2 k = k1 + kz A mass weighing 20 Ib. stretches one spring 5 times as much as it stretches a second spring. The springs are attached to a common rigid support, and the mass is attached in the double- spring configuration, as shown in the figure. The 20-lb mass stretches the entire System by 2 inches, and after the System is set in motion at t = 0, it is known that t = nV3/16 s, the spring is fully compressed to a distance of v3/12 ft from the equilibrium point. k 20 lb A-Determine the value of the effective total constant B-Determine the values of the constants k_1 and k_2 C-Propose a difference equation and the conditions that allow finding the equation of motion of the mass if it is initially released from the equilibrium position with an initial non-zero velocity D-Find the equation of motion of mass E-Determine the initial speed and direction
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