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2 years ago

Compute the solution to x + 2x + 2x = 0 for Xo = 0 mm, vo = 1 mm/s and write down the closed-form expression for the response.

Engineering

1 answer:

Nutka1998 [239]2 years ago

6 0

Answer:

β = $\frac{c}{\sqrt{km} }$ = 0.7071 ≈ 1 ( damping condition )

closed-form expression for the response is attached below

Explanation:

Given : x + 2x + 2x = 0 for Xo = 0 mm and Vo = 1 mm/s

computing a solution :

M = 1,

c = 2,

k = 2,

Wn = $\sqrt{\frac{k}{m} }$ = $\sqrt{2}$

next we determine the damping condition using the damping formula

β = $\frac{c}{\sqrt{km} }$ = 0.7071 ≈ 1

from the condition above it can be said that the damping condition indicates underdamping

attached below is the closed form expression for the response

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Could I please get help with this

alex41 [277]

Answer:

1. $I_{xc}$ = 7.161458 $\overline 3$ in.⁴

$I_{yc}$ = 36.661458 $\overline 3$ in.⁴

Iₓ = 28.6458 $\overline 3$ in.⁴

$I_y$ = 138.6548 $\overline 3$ in.⁴

2. $I_{xc}$ = 114. $\overline 3$ in.⁴

$I_{yc}$ = 37. $\overline 3$ in.⁴

Iₓ = 457. $\overline 3$ in.⁴

$I_y$ = 149. $\overline 3$ in.⁴

3. The maximum deflection of the beam is 2.55552 inches

Explanation:

1. The height of the beam having a rectangular cross section is h = 2.5 in.

The breadth of the beam, is = 5.5 in.

The moment of inertia of a rectangular beam through its centroid is given as follows;

$I_{xc}$ = b·h³/12 = 5.5 × 2.5³/12 = 1375/192 = 7.161458 $\overline 3$

$I_{xc}$ = 7.161458 $\overline 3$ in.⁴

$I_{yc}$ = h·b³/12 = 2.5 × 5.5³/12 = 6655/192 = 36.661458 $\overline 3$

$I_{yc}$ = 36.661458 $\overline 3$ in.⁴

The moment of inertia about the base is given as follows;

Iₓ = b·h³/3 = 5.5 × 2.5³/3 = 625/24 = 28.6458 $\overline 3$

Iₓ = 28.6458 $\overline 3$ in.⁴

$I_y$ = h·b³/3 = 2.5 × 5.5³/3 = 6655/48= 138.6548 $\overline 3$

$I_y$ = 138.6548 $\overline 3$ in.⁴

2. The height of the beam having a rectangular cross section is h = 7 in.

The breadth of the beam, b = 4 in.

The moment of inertia of a rectangular beam through its centroid is given as follows;

$I_{xc}$ = b·h³/12 = 4 × 7³/12 = 114. $\overline 3$

$I_{xc}$ = 114. $\overline 3$ in.⁴

$I_{yc}$ = h·b³/12 = 7 × 4³/12 = 37. $\overline 3$

$I_{yc}$ = 37. $\overline 3$ in.⁴

The moment of inertia about the base is given as follows;

Iₓ = b·h³/3 = 4 × 7³/3 = 457. $\overline 3$

Iₓ = 457. $\overline 3$ in.⁴

$I_y$ = h·b³/3 = 2.5 × 5.5³/3 = 149. $\overline 3$

$I_y$ = 149. $\overline 3$ in.⁴

3. The deflection, $\delta _{max}$ , of a simply supported beam having a point load at the center is given as follows;

$\delta_{max} = \dfrac{W \times L^3}{48 \times E \times I}$

The given parameters of the beam are;

The length of the beam, L = 22 ft. = 264 in.

The applied load at the center, W = 750 lbs

The modulus of elasticity for Cedar = 10,000,000 psi

The height of the wood, h = 3 in.

The breadth of the wood, b = 5 in.

The moment of inertia of the wood, $I_{xc}$ = b·h³/12 = 5 × 3³/12 = 11.25 in.⁴

By plugging in the given values, we have;

$\delta_{max} = \dfrac{750 \times 264^3}{48 \times 10,000,000 \times 11.25} = 2.55552$

The maximum deflection of the beam, $\delta _{max}$ = 2.55552 inches

5 0

3 years ago

Engineering is a broad category that includes a variety of occupations and attempts to solve problems using math and

nadezda [96]

Answer:

Engineering is a broad category that includes a variety of occupations and attempts to solve problems using math and systematic and scientific processes.

Explanation:

Engineering is the scientific discipline that deals with the implementation of science on materials, constructions, machines, systems and processes to realize a specific goal. It is an area of technical activity that includes a number of specialized areas and disciplines aimed at the practical application of scientific, economic, social and practical knowledge in order to turn natural resources for the benefit of humans.

The goals of engineering activities are the invention, development, creation, implementation, repair, maintenance and / or improvement of equipment, materials or processes. Engineering is closely intertwined with science, relying on the postulates of fundamental science and the results of applied research. In this sense, it is a branch of scientific and technical activity.

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3 years ago

The quantity of bricks required increases with the surface area of the wall, but the thickness of a masonry wall does not affect

Yakvenalex [24]

Answer:

false

Explanation:

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3 years ago

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Flip-flops are normally used for all of the following applications, except ________. logic gates data storage frequency division

SpyIntel [72]

Flip-flops are normally used for all of the following applications, except logic gates.

<h3>What are Flip flops?</h3>

Flip flops are known to be tools that are used for counting. They come in different ranges.

Note that Flip flops are one that can be seen on counters, storage registers, and others and as such, Flip-flops are normally used for all of the following applications, except logic gates.

Learn more about Flip flops from

brainly.com/question/4237777

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1 year ago

Convert the unit Decimeter (dm) into Micrometer (um).

oksian1 [2.3K]

Answer:

86701 Micrometers.

Explanation:

Multiply 0.86701 dm by 100,000 to get 86701 um.

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3 years ago