No chstgpt 2. (a) A simple harmonic oscillator's motion is given bythe graph at right. Describing its motion as afunction of time as x(t) = A cos(wt + 0), findits amplitude, angular frequency, and phaseconstant o.** For finding 00, don't just compare to ax (cm)10-5-A-5--1013+(s)calculator. Draw a unit circle or phasor diagram and figure out where the functionmust be at t = 0 to create this graph. Show/explain your work.(b) What is the initial speed of the object, at t = 0? What is the maximum speed of theobject?(c) If this graph represents the position of a 500 g mass on a spring, what is the springconstant? What is the total energy of the system?

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Answered: 2. (a) A simple harmonic oscillator's…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 16PQ

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The expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time, with x in centimeters and t in seconds. What are the a. frequency, b. period, c. amplitude, and d. initial phase of the objects motion? e. What is the position of the particle at t = 1.45 s?
Each piston of an engine makes a sharp sound every other revolution of the engine. (a) How fast is a race car going if its eight-cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per minute is the engine rotating?
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.
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.
Find the frequency of a tuning fork that takes 2.50103 s to complete one oscillation.
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The temperature of the atmosphere oscillates from a maximum near noontime and a minimum near sunrise. Would you consider the atmosphere to be in stable or unstable equilibrium?
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.
(a) If frequency is not constant for some oscillation, can the oscillation be simple harmonic motion? (b) Can you mink of any examples of harmonic motion where the frequency may depend on the amplitude?
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.
A suspension bridge oscillates with an effective force constant of 1.00108 N/m . (a) How much energy is needed to make it oscillate with an amplitude of 0.100 m? (b) If soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart 1.00104 J of energy each second, how long does it take for the bridge’s oscillations to go from 0.100 m to 0.500 m amplitude.

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