Please show full steps /Assignment3.pdfY=-AFigure 1: A mass-spring system.Reference: https://upload.wikimedia.org/wikipedia/commons/8/8d/Oscillation-terms.svg.The function that describes this oscillation in time is of the formY (t) = eat (2 cos(bt) + sin(bt)),where x = a + bi is the solution with b > 0 to the following equationmx? + rx + k = 0.In this equation, m represents the mass in kg, k is the spring constant and measures thespring's elasticity, r measures the friction damping effects.(a) Suppose the mass weighs 10 kg, the spring constant k is 2 and r is 4.Find a and b by solving the quadratic equation.(b) Substitute a and b in the expression for Y(t).(c) Find the initial extension of the spring A = Y(0).(d) Plot Y(t) for positive times. You are allowed to use any graphical software includingWolfram Alpha for this purpose.(e) What do you observe? What will happen for a very large t?4. Population dynamics.In the ski resort, the amount of people visiting changes every day of the year. In the coldo neonle coming, while in the warm period very few are visiting. 3. Dynamics of a spring.Consider the behaviour of a mass-spring system (see Figure 1 below). If it is at equilib-rium, it remains in a rest position. Once it receives a force, it will start oscillating. In thisproblem, we will study the dynamics of these oscillations. We will take as reference the centerof mass and we consider Y = 0 when the system is at rest. We then compress the spring toY = A and study the behaviour of Y in time.IY=AY=0-AY=-AFigure 1: A mass-spring system.Reference: https://upload.wikimedia.org/wikipedia/commons/8/8d/Oscillation-terms.svg.The function that describes this oscillation in time is of the formY (t) = et (2 cos(bt) + sin(bt)),where a = a + bi is the solution with b> 0 to the following equation

Given Function, y(t) = eat (2cosbt + sinbt) ....................(1) And Quadratic Equation, mx2 +…

The function that describes this oscillation in time is of the form Y (t) = eat (2 cos(bt) + sin(bt)), where x a + bi is the solution with b > 0 to the following equation mx + rx+ k = 0. In this equation, m represents the mass in kg, k is the spring constant and measures the spring's elasticity, r measures the friction damping effects. (a) Suppose the mass weighs 10 kg, the spring constant k is 2 and r is 4. Find a and b by solving the quadratic equation. (b) Substitute a and b in the expression for Y(t). (c) Find the initial extension of the spring A = Y(0).

The function that describes this oscillation in time is of the form Y (t) = eat (2 cos(bt) + sin(bt)), where x a + bi is the solution with b > 0 to the following equation mx + rx+ k = 0. In this equation, m represents the mass in kg, k is the spring constant and measures the spring's elasticity, r measures the friction damping effects. (a) Suppose the mass weighs 10 kg, the spring constant k is 2 and r is 4. Find a and b by solving the quadratic equation. (b) Substitute a and b in the expression for Y(t). (c) Find the initial extension of the spring A = Y(0).

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus.

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.

Question

Please show full steps

/Assignment3.pdf
Y=-A
Figure 1: A mass-spring system.
Reference: https://upload.wikimedia.org/wikipedia/commons/8/8d/Oscillation-terms.svg.
The function that describes this oscillation in time is of the form
Y (t) = eat (2 cos(bt) + sin(bt)),
where x = a + bi is the solution with b > 0 to the following equation
mx? + rx + k = 0.
In this equation, m represents the mass in kg, k is the spring constant and measures the
spring's elasticity, r measures the friction damping effects.
(a) Suppose the mass weighs 10 kg, the spring constant k is 2 and r is 4.
Find a and b by solving the quadratic equation.
(b) Substitute a and b in the expression for Y(t).
(c) Find the initial extension of the spring A = Y(0).
(d) Plot Y(t) for positive times. You are allowed to use any graphical software including
Wolfram Alpha for this purpose.
(e) What do you observe? What will happen for a very large t?
4. Population dynamics.
In the ski resort, the amount of people visiting changes every day of the year. In the cold
o neonle coming, while in the warm period very few are visiting.

3. Dynamics of a spring.
Consider the behaviour of a mass-spring system (see Figure 1 below). If it is at equilib-
rium, it remains in a rest position. Once it receives a force, it will start oscillating. In this
problem, we will study the dynamics of these oscillations. We will take as reference the center
of mass and we consider Y = 0 when the system is at rest. We then compress the spring to
Y = A and study the behaviour of Y in time.
I
Y=A
Y=0
-A
Y=-A
Figure 1: A mass-spring system.
Reference: https://upload.wikimedia.org/wikipedia/commons/8/8d/Oscillation-terms.svg.
The function that describes this oscillation in time is of the form
Y (t) = et (2 cos(bt) + sin(bt)),
where a = a + bi is the solution with b> 0 to the following equation

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