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Figure 15.4 shows two curves representing particles undergoing
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- 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_forwardTwo 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_forward
- Provide 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_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_forward
- Clear selection In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, e"max, to the maximum angular velocity, O'max, is Tt s^(-1). What is the time needed for the pendulum to complete two oscillations? O 0.25 sec 1 sec O 0.5 sec O 4 sec 2 sec The equation of motion of a particle in simple harmonic motion is given by: x(t) = O the narticle'sarrow_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_forwardPROBLEM 3: A particle executes simple harmonic motion with an amplitude of 3.00 cm. At what displacement from the midpoint of its motion does the speed equal 1/2 of its maximum speed? PROBLEM 4: An automobile having a mass of 1000 kg is driven into a brick wall in a safety test. The bumper behaves like a spring of constant 5.0 x 10 N/m and compresses 3.16 cm as the car is brought to rest. What was the speed of the car before impact assuming no energy was lost during impact with the wall? PROBLarrow_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
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