 5.1.1: A mass weighing 4 pounds is attached to a spring whose spring const...
 5.1.2: A 20kilogram mass is attached to a spring. If the frequency of sim...
 5.1.3: A mass weighing 24 pounds, attached to the end of a spring, stretch...
 5.1.4: Determine the equation of motion if the mass in is initially releas...
 5.1.5: A mass weighing 20 pounds stretches a spring 6 inches. The mass is ...
 5.1.6: A force of 400 newtons stretches a spring 2 meters. A mass of 50 ki...
 5.1.7: Another spring whose constant is 20 N/m is suspended from the same ...
 5.1.8: A mass weighing 32 pounds stretches a spring 2 feet. Determine the ...
 5.1.9: A mass weighing 8 pounds is attached to a spring. When set in motio...
 5.1.10: A mass weighing 10 pounds stretches a spring foot. This mass is rem...
 5.1.11: A mass weighing 64 pounds stretches a spring 0.32 foot. The mass is...
 5.1.12: A mass of 1 slug is suspended from a spring whose spring constant i...
 5.1.13: Under some circumstances when two parallel springs, with constants ...
 5.1.14: A certain mass stretches one spring foot and another spring foot. T...
 5.1.15: A model of a spring/mass system is 4x
 5.1.16: A model of a spring/mass system is 4x
 5.1.17: In 1720 the given figure represents the graph of an equation of mot...
 5.1.18: In 1720 the given figure represents the graph of an equation of mot...
 5.1.19: In 1720 the given figure represents the graph of an equation of mot...
 5.1.20: In 1720 the given figure represents the graph of an equation of mot...
 5.1.21: A mass weighing 4 pounds is attached to a spring whose constant is ...
 5.1.22: A 4foot spring measures 8 feet long after a mass weighing 8 pounds...
 5.1.23: A 1kilogram mass is attached to a spring whose constant is 16 N/m,...
 5.1.24: In parts (a) and (b) of determine whether the mass passes through t...
 5.1.25: A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 ...
 5.1.26: After a mass weighing 10 pounds is attached to a 5foot spring, the...
 5.1.27: A mass weighing 10 pounds stretches a spring 2 feet. The mass is at...
 5.1.28: A mass weighing 24 pounds stretches a spring 4 feet. The subsequent...
 5.1.29: A mass weighing 16 pounds stretches a spring feet. The mass is init...
 5.1.30: A mass of 1 slug is attached to a spring whose constant is 5 lb/ft....
 5.1.31: A mass of 1 slug, when attached to a spring, stretches it 2 feet an...
 5.1.32: In determine the equation of motion if the external force is f(t) e...
 5.1.33: When a mass of 2 kilograms is attached to a spring whose constant i...
 5.1.34: In write the equation of motion in the form x(t) Asin(vt f) Be2t si...
 5.1.35: A mass m is attached to the end of a spring whose constant is k. Af...
 5.1.36: A mass of 100 grams is attached to a spring whose constant is 1600 ...
 5.1.37: In 37 and 38 solve the given initialvalue problem.
 5.1.38: In 37 and 38 solve the given initialvalue problem.
 5.1.39: (a) Show that the solution of the initialvalue problem is .
 5.1.40: Compare the result obtained in part (b) of with the solution obtain...
 5.1.41: (a) Show that x(t) given in part (a) of can be written in the form ...
 5.1.42: Can there be beats when a damping force is added to the model in pa...
 5.1.43: (a) Show that the general solution of d2x dt2 2 dx dt 2 x F0 sin t ...
 5.1.44: Consider a driven undamped spring/mass system described by the init...
 5.1.45: Find the charge on the capacitor in an LRC series circuit at t 0.01...
 5.1.46: Find the charge on the capacitor in an LRC series circuit when , R ...
 5.1.47: In 47 and 48 find the charge on the capacitor and the current in th...
 5.1.48: In 47 and 48 find the charge on the capacitor and the current in th...
 5.1.49: Find the steadystate charge and the steadystate current in an LRC...
 5.1.50: Show that the amplitude of the steadystate current in the LRC seri...
 5.1.51: Use to show that the steadystate current in an LRC series circuit ...
 5.1.52: Find the steadystate current in an LRC series circuit when , R 20 ...
 5.1.53: Find the charge on the capacitor in an LRC series circuit when , R ...
 5.1.54: Show that if L, R, C, and E0 are constant, then the amplitude of th...
 5.1.55: Show that if L, R, E0, and g are constant, then the amplitude of th...
 5.1.56: Find the charge on the capacitor and the current in an LC circuit w...
 5.1.57: Find the charge on the capacitor and the current in an LC circuit w...
 5.1.58: In find the current when the circuit is in resonance.
Solutions for Chapter 5.1: Linear Models: InitialValue Problems
Full solutions for Differential Equations with BoundaryValue Problems  7th Edition
ISBN: 9780495108368
Solutions for Chapter 5.1: Linear Models: InitialValue Problems
Get Full SolutionsSince 58 problems in chapter 5.1: Linear Models: InitialValue Problems have been answered, more than 15540 students have viewed full stepbystep solutions from this chapter. Differential Equations with BoundaryValue Problems was written by and is associated to the ISBN: 9780495108368. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.1: Linear Models: InitialValue Problems includes 58 full stepbystep solutions. This textbook survival guide was created for the textbook: Differential Equations with BoundaryValue Problems, edition: 7.

Arctangent function
See Inverse tangent function.

Commutative properties
a + b = b + a ab = ba

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Direct variation
See Power function.

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Division
a b = aa 1 b b, b Z 0

Implied domain
The domain of a function’s algebraic expression.

Initial value of a function
ƒ 0.

Linear regression equation
Equation of a linear regression line

Local extremum
A local maximum or a local minimum

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

nth root of unity
A complex number v such that vn = 1

Parametrization
A set of parametric equations for a curve.

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Root of an equation
A solution.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

Xscl
The scale of the tick marks on the xaxis in a viewing window.