1. Suppose we have a spring with attached mass hanging from the ceiling. The vertical displacement of the mass from its equilibrium (where it sits while at rest) can be modeled by the equation y(t) = eat (b cos(ft) + csin(t)). One can determine the coefficients a, b, c and 0, by solving a differential equation which incorporates the mass, spring stiffness, friction and so on, or, we can determine these coefficients by studying some data given by its motion. 1.5 1 0.5 -0.5 -1 fy(t) B D 3 The black curve is y(t), the position of the spring with respect to its equilibrium position. (a) Using the data A = (0, 1), B = (3,0), C = (1,-), D = (3,0) and E = (1, 1), find the corresponding equation for y(t).

1. Suppose we have a spring with attached mass hanging from the ceiling. The vertical displacement of the mass from its equilibrium (where it sits while at rest) can be modeled by the equation y(t) = eat (b cos(ft) + csin(t)). One can determine the coefficients a, b, c and 0, by solving a differential equation which incorporates the mass, spring stiffness, friction and so on, or, we can determine these coefficients by studying some data given by its motion. 1.5 1 0.5 -0.5 -1 fy(t) B D 3 The black curve is y(t), the position of the spring with respect to its equilibrium position. (a) Using the data A = (0, 1), B = (3,0), C = (1,-), D = (3,0) and E = (1, 1), find the corresponding equation for y(t).

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

Work and Heat Transfer

It is generally related to thermal engineering which tells about the use, creation, conversion and transfer of heat energy between the systems. It is also considered that to transfer heat from one source to another, transfer of masses is also required. There are various mechanisms by which, transfer of heat takes place i.e. thermal conduction, convection, radiation or by change of phase. All these mechanisms have their own specific features which sometimes occur simultaneously within the same system.

Question

(b) Using the value for a found in part (a), and without the use of calculus, show that y(t)| ≤ € for all t >
4+ln(2)
In(4)

1. Suppose we have a spring with attached mass hanging from the ceiling. The vertical displacement of the mass from
its equilibrium (where it sits while at rest) can be modeled by the equation
y(t) = e
One can determine the coefficients a, b, c and 0, by solving a differential equation which incorporates the mass, spring
stiffness, friction and so on, or, we can determine these coefficients by studying some data given by its motion.
1.5
1
0.5
-0.5
-1
Ty(t)
e-at (b cos(t) + csin(t)).
TA
B
с.
The black curve is y(t), the position of the spring with respect to its equilibrium position.
(a) Using the data A = (0, 1), B = (3,0), C = (2,-), D = (1, 0) and E = (1, 1), find the corresponding equation for
y(t).

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