Chapter 4: Q1 E (page 227)

In the following problems, take $g = 32 ft / \sec^{2}$ for the U.S. Customary System and role="math" localid="1663948416136" $g = 9.8 m / \sec^{2}$ for the MKS system.
Sketch the frequency response curve (13) for the system in which m = 4, k = 1, b = 2.

Short Answer

Expert verified

Therefore, the frequency response curve is $M (γ) = \frac{1}{\sqrt{{(1 - 4 γ^{2})}^{2} + 4 γ^{2}}}$

Its sketch is shown below;

Step by step solution

General form

The angular frequency:

The amplitude of the steady-state solution to equation (1) depends on the angular frequency of the forcing function and it is given by $A (γ) = F_{0} M (γ)$ , where

$M (γ) : = \frac{1}{\sqrt{{(k - m γ^{2})}^{2} + b^{2} γ^{2}}} \dots (1)$

Evaluate the equation

Given that the frequency response curve is $M (γ) : = \frac{1}{\sqrt{{(k - m γ^{2})}^{2} + b^{2} γ^{2}}}$

And m = 4, k = 1, and b = 2.

Substitute the values in equation (1),

$M (γ) = \frac{1}{\sqrt{{(1 - 4 γ^{2})}^{2} + 4 γ^{2}}}$

Now draw the graph of it.

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In the following problems, take $g = 32 ft / \sec^{2}$ for the U.S. Customary System and role="math" localid="1663948416136" $g = 9.8 m / \sec^{2}$ for the MKS system.
Sketch the frequency response curve (13) for the system in which m = 4, k = 1, b = 2.

Short Answer

Step by step solution

General form

Evaluate the equation

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In the following problems, take g=32ft/sec2for the U.S. Customary System and role="math" localid="1663948416136" g=9.8m/sec2for the MKS system.Sketch the frequency response curve (13) for the system in which m = 4, k = 1, b = 2.

Short Answer

Step by step solution

General form

Evaluate the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Logic and Functions

Pure Maths

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following problems, take $g = 32 ft / \sec^{2}$ for the U.S. Customary System and role="math" localid="1663948416136" $g = 9.8 m / \sec^{2}$ for the MKS system.
Sketch the frequency response curve (13) for the system in which m = 4, k = 1, b = 2.