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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 blocks, with masses M1 = 2.10 kg and M2 = 9.20 kg, and a spring with spring constant k = 463 N/m are arranged on a horizontal, frictionless surface as shown in the Figure. The coefficient of static friction between the two blocks is 0.540. What is the maximum possible amplitude of the simple harmonic motion if no slippage is to occur between the blocks?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_forwardProblem 3: An object oscillates with an angular frequency o = 6 rad/s. At t = 0, the object is at xo = 2.5 cm. It is moving with velocity vx0 = 14 cm/s in the positive x-direction. The position of the object can be described through the equation x(t) = A cos(@t + o). Part (a) What is the the phase constant o of the oscillation in radians? (Caution: If you are using the trig functions in the palette below, be careful to adjust the setting between degrees and radians as needed.) sin() cos() tan() 7 8 HOME cotan() asin() acos() 4 5 atan() acotan() sinh() 1 2 3 cosh() tanh() cotanh() END ODegrees O Radians vol BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Part (b) Write an equation for the amplitude A of the oscillation in terms of x, and o. Use the phase shift as a system parameter. Part (c) Calculate the value of the amplitude A of the oscillation in cm.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
- In Problems 1 to 6 find the amplitude, period, frequency, and velocity amplitude for the motion of a particle whose distance s from the origin is the given function. 1. s= 3 cos 5t 2. s= 2 sin(4t – 1) 3. s = cos(rt-8) 4. s=5 sin(t- 7) 5. s = 2 sin 3t cos 3t 6. 8 = 3 sin(2t + 7/8) + 3 sin(2t – 7/8) %3Darrow_forwardthe 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_forwardClear 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_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