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 3.3P
(a)
To determine
The maximum displacement.
(b)
To determine
The maximum potential energy.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The equation of motion for a damped harmonic oscillator is s(t) = Ae^(−kt) sin(ωt + δ),where A, k, ω, δ are constants. (This represents, for example, the position of springrelative to its rest position if it is restricted from freely oscillating as it normally would).(a) Find the velocity of the oscillator at any time t.(b) At what time(s) is the oscillator stopped?
Consider a simple harmonic oscillator consisting of a one kilogram mass m' on a spring with spring/forceconstant k and length L'. If the mass of the spring ms is 9% of the attached mass, and k = 66 N/m,and if we determined the attached body is displaced 3 cm and given a downward velocity of 0.4 m/s -calculate,→ the frequency ω of the motion, ,→ and the amplitude A of the motion
Consider a bob attached to a vertical string. At t = 0, the bob is displaced to a new position where thestring makes −8° with the vertical and is then released from rest. If the angular displacement θ(t) iswritten as a cosine function, then the phase constant φ is:
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
- Let the initial position and speed of an overdamped, nondriven oscillator be x0 and v0, respectively. (a) Show that the values of the amplitudes A1 and A2 in Equation 3.44 have the values A1=2x0+v021 and A2=1x0+v021 where 1 = 2 and 2 = + 2. (b) Show that when A1 = 0, the phase paths of Figure 3-11 must be along the dashed curve given by x=2x, otherwise the asymptotic paths are along the other dashed curve given by x=1x. Hint: Note that 2 1 and find the asymptotic paths when t .arrow_forwardObtain the response of a linear oscillator to a step function and to an impulse function (in the limit τ → 0) for overdamping. Sketch the response functions.arrow_forwardShow that, if a driven oscillator is only lightly damped and driven near resonance, the Q of the system is approximately Q2(TotalenergyEnergylossduringoneperiod)arrow_forward
- The maximum velocity attained by the mass of a simple harmonic oscillator is 10 cm/s, and the period of oscillation is 2 s. If the mass is released with an initial displacement of 2 cm, find (a) the amplitude, (b) the initial velocity, (c) the maximum acceleration, and (d) the phase angle.arrow_forwardFind g at a point on earth where T=2.01 s for a simple pendeulum of length 1.00 m, undergoing small-amplitude-oscillations.arrow_forwardExplain the term amplitude as it relates to the graph of asinusoidal function.arrow_forward
- Two springs of force constants k1 and k2 are attached to a block of mass m and to fixed supports as shown in Fig. 2. The table surface is frictionless. (a) If the block is displaced from its equilibrium position and is then released, show that its motion will be simple harmonic with angular frequency w = √(k1 + k2)/m. (b) Suppose the system is now submersed in a liquid with damping coefficient b , what is the condition that the block will return to itsequilibrium position without oscillation?Sketch a graph to show the behavior of the system in this case.arrow_forwardThe maximum velocity attained by the mass of a simple harmonic oscillator is 10 cm/s, andthe period of oscillation is 2 s. If the mass is released with an initial displacement of 2 cm,find the following:a. the initial velocityb. the maximum accelerationarrow_forwardLet's consider a simple pendulum, consisting of a point mass m, fixed to the end of a massless rod of length l, whose other end is fixed so that the mass can swing freely in a vertical plane. The pendulum's position can be specified by its angle Φ from the equilbrium position. Prove that the pendulum's potential energy is U(ϕ)=mgl(1−cosϕ). Write down the total energy E as a function of Φ and ϕ˙. Show that by differentiating E with respect to t you can get the equation of motion for Φ. Solve for Φ(t). If you solve properly, you should find periodic motion. What is the period of the motion?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning