Advanced Engineering Mathematics [1367744] 5th. Edition by Dennis G. Zill, Warren S. Wright | 9781449679774 | 1449679773 | Holooly

Advanced Engineering Mathematics [1367744]

438 SOLVED PROBLEMS

Question: 3.8.6

Interpret and solve the initial-value problem 1/5 d²x/dt² + 1.2 dx/dt + 2x 5 cos 4t, x(0) 1/2, x'(0) 0. (26) ...

Verified Answer:

We can interpret the problem to represent a vibrat...

Question: 9.12.6

Evaluate the line integral in Example 4. ...

Verified Answer:

One method of evaluating the line integral is to w...

Question: 8.6.7

Use the inverse of the coefficient matrix to solve the system 2×1 + x3 = 2 -2×1 + 3×2 + 4×3 = 4 -5×1 + 5×2 + 6×3 = -1 ...

Verified Answer:

We found the inverse of the coefficient matrix [l...

Question: 8.2.5

Solve the linear system in Example 2 using (a) Gaussian elimination and (b) Gauss-Jordan elimination. ...

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(a) Using row operations on the augmented matrix o...

Question: 8.2.2

Solve 2×1 + 6×2 + x3 = 7 x1 + 2×2 – x3 = -1 5×1 + 7×2 – 4×3 = 9. ...

Verified Answer:

We begin by interchanging the first and second row...

Question: 4.2.5

Solve y” – 3y’ + 2y e^-4, y(0) 1, y'(0) 5. ...

Verified Answer:

Proceeding as in Example 4, we transform the DE by...

Question: 3.8.8

Solve the initial-value problem d²x/dt² + ω²x = F0 sin γt, x(0) = 0, x’ (0) = 0, (29) where F0 is a constant and γ ≠ ω. ...

Verified Answer:

The complementary function is

x_c(t)=c_1 \c...

Question: 3.8.5

A 16-pound weight is attached to a 5-foot-long spring. At equilibrium the spring measures 8.2 feet. If the weight is pushed up and released from rest at a point 2 feet above the equilibrium position, find the displacements x(t) if it is further known that the surrounding medium offers a resistanc ...

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The elongation of the spring after the weight is a...

Question: 3.8.4

An 8-pound weight stretches a spring 2 feet. Assuming that a damping force numerically equal to two times the instantaneous velocity acts on the system, determine the equation of motion if the weight is released from the equilibrium position with an upward velocity of 3 ft/s . ...

Verified Answer:

From Hooke’s law we see that 8 = k(2) gives k = 4 ...

Question: 3.8.1

A mass weighing 2 pounds stretches a spring 6 inches. At t = 0 the mass is released from a point 8 inches below the equilibrium position with an upward velocity of 4\3 ft/s. Determine the equation of free motion. ...

Verified Answer:

Because we are using the engineering system of uni...

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