Swing is a mass hanging by a spring under the influence of gravity. The force due to gravity, F., is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount yi. The gravitational constant g, is 9.81 m/s². Your tasks: No Deflection y m Fg = mg Initial Condition www m k Fg = mg Figure 3: System schematic for Problem 4. A Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. (2 B Write down an expression for the total energy H as the sum of potential and kinetic energy in terms of y, y, yi and element parameters. Will H change as the mass moves? C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of position, y, the initial deflection y, and other constants ( D What would happen to H as the system moves if a dampening element c is added in parallel to the spring?

Swing is a mass hanging by a spring under the influence of gravity. The force due to gravity, F., is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount yi. The gravitational constant g, is 9.81 m/s². Your tasks: No Deflection y m Fg = mg Initial Condition www m k Fg = mg Figure 3: System schematic for Problem 4. A Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. (2 B Write down an expression for the total energy H as the sum of potential and kinetic energy in terms of y, y, yi and element parameters. Will H change as the mass moves? C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of position, y, the initial deflection y, and other constants ( D What would happen to H as the system moves if a dampening element c is added in parallel to the spring?

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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