Concept explainers
Figure 15.4 shows two curves representing particles undergoing
Trending nowThis is a popular solution!
Chapter 15 Solutions
Physics for Scientists and Engineers, Volume 2
Additional Science Textbook Solutions
Essential University Physics (3rd Edition)
Introduction To Health Physics
Conceptual Physical Science (6th Edition)
University Physics Volume 1
The Cosmic Perspective (8th Edition)
- 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.arrow_forwardA simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.arrow_forwardThe total energy of a simple harmonic oscillator with amplitude 3.00 cm is 0.500 J. a. What is the kinetic energy of the system when the position of the oscillator is 0.750 cm? b. What is the potential energy of the system at this position? c. What is the position for which the potential energy of the system is equal to its kinetic energy? d. For a simple harmonic oscillator, what, if any, are the positions for which the kinetic energy of the system exceeds the maximum potential energy of the system? Explain your answer. FIGURE P16.73arrow_forward
- 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.arrow_forwardFigure 12.4 shows two curves representing particles undergoing simple harmonic motion. The correct description of these two motions is that the simple harmonic motion of particle B is (a) of larger angular frequency and larger amplitude than that of particle A, (b) of larger angular frequency and smaller amplitude than that of particle A, (c) of smaller angular frequency and larger amplitude than that of particle A, or (d) of smaller angular frequency and smaller amplitude than that of particle A. Figure 12.4 (Quick Quiz 12.3) Two xt graphs for particles undergoing simple harmonic motion. The amplitudes and frequencies are different for the two particles.arrow_forwardProblem 1: A particle undergoes simple harmonic motion with a frequency of f, = 10 Hz. At t = 0 ; the position of the particle is x(0) = 0.25 m, and the velocity of the particle is v(0) = 0.1 m/s a- Calculate the angular frequency of the oscillation (wo = ??) b- Find the amplitude of the oscillation (A = ??) c- Determine the phase f from the initial conditions (f=??) d- Find the displacement x at any time t. (x(t) = ??)arrow_forward
- Two particles oscillate in simple harmonic motion with amplitude A about the centre of a common straight line of length 2A. Each particle has a period of 1.5 s, and their phase constants differ by 4 rad. (a) How far apart are the particles (in terms of A) 0.5 s after the lagging particle leaves one end of the path? Enter the exact answer in terms of A. ab sin (a) Ωarrow_forwardProvide a detailed explanation please.arrow_forwardA particle undergoes a simple harmonic motion with an amplitude A and a total energy E. When the displacement is one-fourth the amplitude (x = + A/4), the ratio of the kinetic energy, K, to the total energy, E, is: K/E = 8/9 K/E = 1/16 K/E = 1/4 K/E = 1/9 K/E = 15/16 O K/E = 3/4 A block-spring system is in simple harmonic motion on a frictionless horizontalarrow_forward
- the general solution to a harmonic oscillator are related. There are two common forms for the general solution for the position of a harmonic oscillator as a function of time t: 1. x(t) = A cos (wt + p) and 2. x(t) = C cos (wt) + S sin (wt). Either of these equations is a general solution of a second-order differential equation (F= mā); hence both must have at least two--arbitrary constants--parameters that can be adjusted to fit the solution to the particular motion at hand. (Some texts refer to these arbitrary constants as boundary values.) Part D Find analytic expressions for the arbitrary constants A and in Equation 1 (found in Part A) in terms of the constants C and Sin Equation 2 (found in Part B), which are now considered as given parameters. Express the amplitude A and phase (separated by a comma) in terms of C and S. ► View Available Hint(s) Α, φ = V ΑΣΦ ?arrow_forwardA physical pendulum composed of a solid sphere with radius R = 0.500m, is hanged from a ceiling by string of length equal to radius. What are the (a) angular frequency, (b) period, (c) frequency of the system for small angles of oscillation? For solid sphere Icm = 2/5 mr2. Also, why is the distance of the center of mass of the system from the point of oscillation 3R/2?arrow_forwardA 5.0 kg block is attached to a spring of spring constant k=4.00x10^2 N/m and undergoes simple harmonic motion along a frictionless, horizontal tabletop. A second 3.0 kg block sits on top of the first block as shown. The coeffcient of static friction between the two blocks is μs=0.25. What is the greatest amplitude the blocks can undergo without the second block sliding off ? Look at image for refrence. Show all work.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning