A mass of 1 kg stretches a spring by 20 cm. Neglect damping constant, an external vibrations create a force of F(t)=10cos2t N. Note: Round all answers to 1 decimal place. 1. Find the steady-state solution. u(t)= 2. Find the amplitude. A= 3. Find the phase shift. 8 =

A mass of 1 kg stretches a spring by 20 cm. Neglect damping constant, an external vibrations create a force of F(t)=10cos2t N. Note: Round all answers to 1 decimal place. 1. Find the steady-state solution. u(t)= 2. Find the amplitude. A= 3. Find the phase shift. 8 =

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Description: A Moving to another question will save this response.Question 3A mass of 1 kg stretches a spring by 20 cm. Neglect damping constant,an external vibrations create a force of F(t)=10 cos 2t N.Note: Round all answers to 1 decimal place.1. Find the stea

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter4: Nonlinear Oscillations And Chaos

Section: Chapter Questions

Problem 4.24P

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Allow the motion in the preceding problem to take place in a resisting medium. After oscillating for 10 s, the maximum amplitude decreases to half the initial value. Calculate (a) the damping parameter β, (b) the frequency υ1 (compare with the undamped frequency υ0), and (c) the decrement of the motion.
Suppose you have a 0.750-kg object on a horizontal surface connected to a spring that has a force constant of 150 N/m. There is simple friction between the object and surface with a static coefficient of friction s=0.100 . (a) How far can the spring be stretched without moving the mass? (b) If the object is set into oscillation with an amplitude twice the distance found in part (a), and the kinetic coefficient of friction is k=0.0850 , what total distance does it travel before stopping? Assume it starts at the maximum amplitude.
A baby bounces up and down in her crib. Her mass is 12.5 kg, and the crib mattress can be modeled as a light spring with force constant 700 N/m. (a) The baby soon learns to bounce with maximum amplitude and minimum effort by bending her knees at what frequency? (b) If she were to use the mattress as a trampoline losing contact with it for part of each cyclewhat minimum amplitude of oscillation does she require?
(a) If frequency is not constant for some oscillation, can the oscillation be simple harmonic motion? (b) Can you mink of any examples of harmonic motion where the frequency may depend on the amplitude?
(a) If frequency is not constant for some oscillation, can the oscillation be SHM? (b) Can you think of any examples of harmonic motion where the frequency may depend on the amplitude?
A suspension bridge oscillates with an effective force constant of 1.00108 N/m . (a) How much energy is needed to make it oscillate with an amplitude of 0.100 m? (b) If soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart 1.00104 J of energy each second, how long does it take for the bridge’s oscillations to go from 0.100 m to 0.500 m amplitude.
Suppose you have a 0.750kg object on a horizontal surface connected to a spring that has a force constant of 150N/m. There is simple friction between me object and surface with a static coefficient of friction =0.100. (a) How far can the spring be stretched without moving the mass? (b) If the object is set into oscillation with an amplitude twice the distance found in part (a), and me kinetic coefficient of friction is k=0.0850, what total distance does it travel before stopping? Assume it starts at me maximum amplitude.
A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where U0 and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.
C, N A uniform plank of length L and mass M is balanced on a fixed, semicircular bowl of radius R (Fig. P16.19). If the plank is tilted slightly from its equilibrium position and released, will it execute simple harmonic motion? If so, obtain the period of its oscillation.
The equations listed in Table 2.2 give position as a function of time, velocity as a function of time, and velocity as a function of position for an object moving in a straight line with constant acceleration. The quantity vxi appears in every equation. (a) Do any of these equations apply to an object moving in a straight line with simple harmonic motion? (b) Using a similar format, make a table of equations describing simple harmonic motion. Include equations giving acceleration as a function of time and acceleration as a function of position. State the equations in such a form that they apply equally to a blockspring system, to a pendulum, and to other vibrating systems. (c) What quantity appears in every equation?
The expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time, with x in centimeters and t in seconds. What are the a. frequency, b. period, c. amplitude, and d. initial phase of the objects motion? e. What is the position of the particle at t = 1.45 s?
An undamped driven harmonic oscillator satisfies the equation of motion m(d2x/dt2+ 02x) = F(t). The driving force F(t) = F0 sin(t) is switched on at t= 0. (a) Find x(t) for t 0 for the initial conditions x = 0 and v = 0 at t = 0. (b) Find x(t) for = 0 by taking the limit 0 in your result for part (a). Sketch your result for x(t). Hint: In part (a) look for a particular solution of the differential equation of the form x = A sin(t) and determine A. Add the solution of the homogeneous equation to this to obtain the general solution of the inhomogeneous equation.