Chapter 4: Q3 E (page 210)

Try to predict the qualitative features of the solution to $y - 6 y^{2} = 0$ that satisfies the initial conditions $y (0) = - 1, y' (0) = - 1$ . Compare with the computer-generated Figure 4.23. [Hint: Consider the sign of the spring stiffness]

Short Answer

Expert verified

The sign of the stiffness constant is negative. And, stiffness is $k = - 6 y$ . Then, the initial conditions both are negative and compared with computer-generated figure the stiffness reverses the negative velocity and restores to zero.

Step by step solution

General form

The mass–spring oscillator equation

$F_{ext} = [inertia] y + [damping] y' + [stiffness] y = my + by' + ky$ ......(1)

Evaluate the given equation

Given that, $y - 6 y^{2} = 0$ and $y (0) = - 1, y' (0) = - 1$ .

Compare the given equation with equation (1) to get stiffness.

Here, the stiffness is negativelocalid="1663956016989" $k = - 6 y$ and negative sign indicates it lends to reinforce, rather than oppose, displacement.

Then, the initial conditions are both negative. So, the stiffness reverses the negative velocity and restores it to zero.

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Try to predict the qualitative features of the solution to $y - 6 y^{2} = 0$ that satisfies the initial conditions $y (0) = - 1, y' (0) = - 1$ . Compare with the computer-generated Figure 4.23. [Hint: Consider the sign of the spring stiffness]

Short Answer

Step by step solution

General form

Evaluate the given equation

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Try to predict the qualitative features of the solution to y-6y2=0that satisfies the initial conditions y0=-1,y'0=-1. Compare with the computer-generated Figure 4.23. [Hint: Consider the sign of the spring stiffness]

Short Answer

Step by step solution

General form

Evaluate the given equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Pure Maths

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Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Try to predict the qualitative features of the solution to $y - 6 y^{2} = 0$ that satisfies the initial conditions $y (0) = - 1, y' (0) = - 1$ . Compare with the computer-generated Figure 4.23. [Hint: Consider the sign of the spring stiffness]