V1A mass of 0.50 kg is in harmonic horizontal friction-free oscillation with a spring. Theoscillations cover a total distance of 0.500 m. The oscillation can be described by the formulax(t) = Acos(@t+). The acceleration is ax= -0.60 m/s² when the mass is at x = 0.020 m.wwwwwwwwwm = 0.50 kgxx = 0 x = 0.020 ma) What is the phase angle if x=0.14 m at t=0 s? (1 p)b) What is the spring constant ? (2 p)c) What is the kinetic energy at x = 0.14 m? (1 p)در

Given:mass of the object (m) = 0.5 kgTotal distance covered by the object in the oscillation (d) =…

Answered: V1 A mass of 0.50 kg is in harmonic…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 12OQ

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We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
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The equation of motion of a simple harmonic oscillator is given by x(t) = (18.0 cm) cos (10t) (16.0 cm) sin (10t), where t is in seconds. a. Find the amplitude. b. Determine the period. c. Determine the initial phase.
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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.
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?

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