Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 3, Problem 3.19P
To determine
Show that
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
deal with a mass-spring-dashpot sys-
tem having position function x(t) satisfying Eq. (4). We write
xo = x (0) and vo = x'(0) and recall that p = c/(2m), w
k/m, and wi = wổ – p². The system is critically damped,
overdamped, or underdamped, as specified in each problem.
Probler
24. (Critically damped) Show in this case that
x(1) = (xo + voi + pxot)e¬P!.
To be able to solve rectilinear problems with variable functions.
A particle moves with harmonic motion over a path 10in long in 10sec. Find A, V and t when it has moved 5in from one end.
Anisotropic Oscillator Consider a two-dimensional anisotropic oscillator is rational (that is, ws/wy = p/q 4. Prove that if the ratio of the frequencies w and wy where p and q are integers with gcd(p, q) = 1, where gcd stands for greatest common divisor) then the motion is periodic. Determine the period. P
Chapter 3 Solutions
Classical Dynamics of Particles and Systems
Ch. 3 - Prob. 3.1PCh. 3 - Allow the motion in the preceding problem to take...Ch. 3 - Prob. 3.3PCh. 3 - Prob. 3.4PCh. 3 - Obtain an expression for the fraction of a...Ch. 3 - Two masses m1 = 100 g and m2 = 200 g slide freely...Ch. 3 - Prob. 3.7PCh. 3 - Prob. 3.8PCh. 3 - A particle of mass m is at rest at the end of a...Ch. 3 - If the amplitude of a damped oscillator decreases...
Ch. 3 - Prob. 3.11PCh. 3 - Prob. 3.12PCh. 3 - Prob. 3.13PCh. 3 - Prob. 3.14PCh. 3 - Reproduce Figures 3-10b and c for the same values...Ch. 3 - Prob. 3.16PCh. 3 - For a damped, driven oscillator, show that the...Ch. 3 - Show that, if a driven oscillator is only lightly...Ch. 3 - Prob. 3.19PCh. 3 - Plot a velocity resonance curve for a driven,...Ch. 3 - Let the initial position and speed of an...Ch. 3 - Prob. 3.26PCh. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - Prob. 3.29PCh. 3 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Obtain the response of a linear oscillator to a...Ch. 3 - Calculate the maximum values of the amplitudes of...Ch. 3 - Consider an undamped linear oscillator with a...Ch. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - An automobile with a mass of 1000 kg, including...Ch. 3 - Prob. 3.41PCh. 3 - An undamped driven harmonic oscillator satisfies...Ch. 3 - Consider a damped harmonic oscillator. After four...Ch. 3 - A grandfather clock has a pendulum length of 0.7 m...
Knowledge Booster
Similar questions
- A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass is slowly lifted along a circular arc to a height h. a. Assuming the only force acting on the mass is the gravitational force, show that the component of this force acting along the arc of motion is F = mg sin u. b. Noting that an element of length along the path of the pendulum is ds = L du, evaluate an integral in u to show that the work done in lifting the mass to a height h is mgh.arrow_forward4.30. No damping force * A particle of mass m is subject to a spring force, -kx, and also a driving force, Fa cos wat. But there is no damping force. Find the particular solution for x(t) by guessing x(t) = A cos wat + B sin wat. If you write this in the form C cos(wat - o), where C > 0, what are C and o? Be careful about the phase (there are two cases to consider).arrow_forwardProb.1 (i) State the required conditions of simple harmonic motion (SHH). (ii) Consider the torsional pendulum with a moment of inertia I and torsion constant K. If the pendulum starts its oscillation with an initial angle O, and angular at t = 0. Obtain the equation of motion and angular frequency of dt de velocity j %3D oscillation w. for this pendulum and discuss that it can be classified as SHH. Show that the torsional angle and angular velocity a of the pendulum for all time can be expressed as (iii) sin wt 0 (t) = 0; coS wt + w(t) = -w0; sin wt + w cos wt .arrow_forward
- Consider the function ƒ(x) = 4 sin(( 3)) + 6. State the amplitude A. period P 2 A, a midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum a N minimum y-values and their corresponding a-values. Enter the exact answers. Amplitude: A = 4 Period: P = Bù Midline: y = Number The phase shift is Click for List The vertical translation is Click for List 1 Hints for the maximum and minimum values of f(x): π and = 2 프 The maximum value of y = sin(x) is y = 1 and the corresponding a values are x multiples of 2 7 less than and more than this a value. You may want to solve ( x − 3) = 2 3T and • The minimum value of u = sin (r) is 71 sin (r) is = -1 and the corresponding r values are Submit Assignment Quit & Savearrow_forwardAn undamped harmonic oscillator of mass m and spring constant k oscillates with an amplitude A. In terms of A, at what postion x is the speed of the oscillator, v, is half of its maximum speed v, max Hint: Set-up the energy equation at any postion. What is the maximum energy of the oscillator?arrow_forwarddy dt 10. The equation of motion of a mechanical system is 4+ 10y = 120g (t) where g(t) is the stimulus or input applied to the system and y(t) is its output. Assume the system is quiescent. i. Find the transfer function of the system and the pole. ii. If a step of unit height is applied at the input, in the Laplace domain, find the system output, y(s), using partial fractions. Hence determine the time domain output of the system, y(t). iii.arrow_forward
- Need help on D). I can't seem to get the correct answer. My answers are 24.9, .264 and 24.87 and none of them work in the program. See below The net x-force on a 1-kg oscillating object moving along the x axis is Fx = −b(x − a2x3), where b = 123 and a = 4 in the appropriate SI units.(a) What are the units of a and b?a) Unit of a is _1/m____ (Click to select) 1/m m N*m 1/N N/m N b) Unit of b is _______N/M (Click to select) m/N N N/m 1/m 1/N m N*m . For small oscillations, the force law reduces to the harmonic oscillator law F x ≈≈−k sx, where ks depends on the value of a and/or b.C) What is the frequency of such small oscillations?( Round the answer to two decimal places.)The frequency is 1.77 Hz. (d) How small is "small"? For what range of x will Fx be within 1% of −ksx ? ____cmarrow_forwardA mass of 458 g stretches a spring by 7.2 cm. The damping constant is c = 0.34. External vibrations create a force of F(t)= 0.4 sin 5t Newtons, setting the spring in motion from its equilibrium position with zero velocity. What is the imaginary part v, of the complex root of the homogeneous equation? Use g-9.8. Express your answer in two decimal places.arrow_forwardFunction y 2(sin(4x – 7) – 4) , determine its amplitude, phase shift and period.arrow_forward
- As an illustration of why it matters which variables you hold fixed when taking partial derivatives, consider the following mathematical example. Let w = xy and x = yz. Write w purely in terms of x and z, and then purely in terms of y and z.arrow_forwardAn electron undergoes simple harmonic motion with the acceleration shown below: ax(t)=−amaxsin(2t/T) with amax=5839 ms2 and T=316 seconds. Assuming that the only motion is oscillatory (ignoring overall translation), what is the maximum speed of the electron? What is the amplitude of the electron's position?arrow_forwardProblem 3: The motion of critically damped and overdamped oscillator systems is hardly "oscillatory". (a) To illustrate this, prove that a critically damped oscillator passes through the originx = 0 at most once, and determine the relationship between the initial conditions To and vo that is required for the oscillator to pass through the origin. (b) Do the same thing for the overdamped oscillator.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON