Answered: Which of the following could represent…

Which of the following could represent the horizontal component of the net force of a simple harmonic oscillator with x being the displacement measured from the equilibrium point?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A block of mass m = 2 kg is attached a spring of force constant k = 500 N/m as shown in the figure below.The block is initially at the equilibrium point at x = 0 m where the spring is at its natural length. Then theblock is set into a simple harmonic oscillation with an initial velocity 2.5 m/s at x = 0 cm towards right. Thehorizontal surface is frictionless. a) What is the period of block’s oscillation? b) Find the amplitude A of the oscillation, which is the farthest length spring is stretched to. c) Please represent block’s motion with the displacement vs. time function x(t) and draw the motion graphx(t) for at least one periodic cycle. Note, please mark the amplitude and period in the motion graph.Assume the clock starts from when the block is just released. d) Please find out the block’s acceleration when it is at position x = 5cm. e) On the motion graph you draw for part c), please mark with diamonds ♦ where the kinetic energy of theblock is totally transferred to the spring…
Problem 5: (a) For a driven, damped harmonic oscillator, the peak of the amplitude (and therefore the maximum potential energy) occurs for a driving frequency of w=w₂ = √3 - 2/3². Determine the driving frequency at which the kinetic energy of the system is a maximum. (b) Make a "resonance peak" plot of kinetic energy versus driving frequency, for various values of ß. [You may assume that wo = 1 rad/s, or equivalently you can choose to measure driving frequency w and damping / as fractions or multiples of wo. Choose a convenient value for the driving force.]
(1) What is the resonant frequency of a damped harmonic oscillator whose mass m = 440. grams, force constant k = 370. N/m, with a viscous damping force that is linearly proportional to the speed with constant c = 7.80 N s/m? (2)What is the steady state amplitude of this oscillator when driven by a sinusoidal driving force of amplitude 22.0 N and frequency w = 25.0 rad/s?
Consider a simple harmonic oscillator with natural frequency, w = 1 and the displacement from equilibrium of the mass is denoted by x. At t=0, the mass is released from x=1m with speed 2m/s. What is the magnitude of x at time, t= s?
The equation of motion for a damped harmonic oscillator is s(t) = Ae^(−kt) sin(ωt + δ),where A, k, ω, δ are constants. (This represents, for example, the position of springrelative to its rest position if it is restricted from freely oscillating as it normally would).(a) Find the velocity of the oscillator at any time t.(b) At what time(s) is the oscillator stopped?
Problem 3: The motion of critically damped and overdamped oscillator systems is hardly "oscillatory". (a) To illustrate this, prove that a critically damped oscillator passes through the originx = 0 at most once, and determine the relationship between the initial conditions To and vo that is required for the oscillator to pass through the origin. (b) Do the same thing for the overdamped oscillator.
Consider a mass m attached to a spring with natural length 7, hanging vertically under the action of gravity mgk (where the unit vector k is pointing downwards) and a constant friction force F =-Fok. (a) Find the equilibrium point of the mass, write the equation of motion, and show that the motion of the particle is governed by the fundamental equation of simple harmonic motion. (b) Assume the particle is released from the spring when it has heighth above ground and initial velocity vo. Let y be the height above ground of the particle (note that the orientation of the axis is now opposite of z used in point (a)). Write the equation of motion (under the action of gravity and the friction force F). Solve them for the given initial condition and show that v(y)² = vz+2(g− ¹)(h—−y) m (c) Upon entering the ground (y=0) with velocity v₁, the particle is subject to a constant friction force F₁ where F₁ >0 is a constant. Calculate the distance d travelled by the particle into the ground in…
A mass m = 2.07 kg is attached to a spring of force constant k = 46.9 N/m and set into oscillation on a horizontal frictionless surface by stretching it an amount A = 0.19 m from its equilibrium position and then releasing it. The figure below shows the oscillating mass and the particle on the associated reference circle at some time after its release. The reference circle has a radius A, and the particle traveling on the reference circle has a constant counterclockwise angular speed w, constant tangential speed V = wA, and centripetal acceleration of constant magnitude a. w²A. (a) Determine the following. maximum speed of the oscillating mass m/s magnitude of the maximum acceleration of the oscillating mass +A m/s2 x =-A V = @A magnitude of the maximum force experienced by the oscillating mass N a̟= w³A ot maximum kinetic energy of the oscillating mass maximum elastic potential energy of the spring attached to the mass total energy of the oscillating mass-spring system (c) If the…
A simple harmonic oscillator is at equilibrium when the mass is at position x =0. The mass ispulled to x = +12 cm and released from rest.Rank the speed of the mass when it is at the following positions from least to greatest.
(d)/ = 4f The following given is for questions 3 and 4: A block of mass m= 2 kg is attached to a spring with spring constant k= 200 N/m, and set to oscillates on a frictionless horizontal surface. At time t= 0 its position is x, = 0 and its velocitty is Vo = +5 m/s. 3) Which of the following is true about the oscillation amplitude and the phase constant, e (a)A= 0.5, =/2. (b)A = 0.5, e-/2) (c) A = 0.25, =/2 (d)A = 0.25, p7/2 stiocles the pOssible values ol 4) When the block's velocty lis (a) x = +(3/4)A e o ch
(a) Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.) (b)Write an equation that represents the curve in the form
What type of force F(x) will produce simple harmonic oscillation?