Chapter 4: Q2 E (page 227)

In the following problems, take $g = 32 ft / \sec^{2}$ for the U.S. Customary System $g = 9.8 m / \sec^{2}$ and for the MKS system.
Sketch the frequency response curve (13) for the system in which m = 2, k = 3, b = 3.

Short Answer

Expert verified

Therefore, the frequency response curve is $M (γ) = \frac{1}{\sqrt{{(3 - 2 γ^{2})}^{2} + 9 γ^{2}}}$ . and 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 = 2, k = 3, and b = 3.

Substitute the values in equation (1).

$M (γ) = \frac{1}{\sqrt{{(3 - 2 γ^{2})}^{2} + 9 γ^{2}}}$

Now draw the graph for it.

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In the following problems, take $g = 32 ft / \sec^{2}$ for the U.S. Customary System $g = 9.8 m / \sec^{2}$ and for the MKS system.
Sketch the frequency response curve (13) for the system in which m = 2, k = 3, b = 3.

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 Systemg=9.8m/sec2 and for the MKS system.Sketch the frequency response curve (13) for the system in which m = 2, k = 3, b = 3.

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

Decision Maths

Applied Mathematics

Discrete Mathematics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following problems, take $g = 32 ft / \sec^{2}$ for the U.S. Customary System $g = 9.8 m / \sec^{2}$ and for the MKS system.
Sketch the frequency response curve (13) for the system in which m = 2, k = 3, b = 3.