In the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. Separation L = 1.3 m, linear density μ = 1.1 g/m, and the oscillator frequency f= 190 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q. (a) What mass m allows the oscillator to set up the fourth harmonic on the string? (b) What standing wave mode, if any, can be set up if m= 2 kg (Give 0 if the mass cannot set up a standing wave)? Oscillator ge

In the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. Separation L = 1.3 m, linear density μ = 1.1 g/m, and the oscillator frequency f= 190 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q. (a) What mass m allows the oscillator to set up the fourth harmonic on the string? (b) What standing wave mode, if any, can be set up if m= 2 kg (Give 0 if the mass cannot set up a standing wave)? Oscillator ge

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 mass of 0.38 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.26 m)cos[(16 rad/s)t]. Determine the following. %3D (a) amplitude of oscillation for the oscillating mass How does the amplitude of oscillation compare to the magnitude of the maximum displacement from equilibrium? m (b) force constant for the spring N/m (c) position of the mass after it has been oscillating for one half a period m (d) position of the mass one-third of a period after it has been released (e) time it takes the mass to get to the position x = -0.10 m after it has been released
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…
Part 2) An organ pipe of length L = 4.6 m is open at both ends. It is driven to oscillate with a standing wave that has two nodes within the pipe. (a) What is the wavelength of the standing wave? m (b) If the speed of sound in air is 330m/s, what is the frequency that the organ pipe is oscillating at in this mode? Hz
In the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. Separation L = 0.8 m, linear density μ = 1.6 g/m, and the oscillator frequency f = 200 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q.(a) What mass m allows the oscillator to set up the fourth harmonic on the string?(b) What standing wave mode, if any, can be set up if m = 4 kg (Give 0 if the mass cannot set up a standing wave)?
A disk of radius 0.25 meters is attached at its edge to a light (massless) wire of length 0.50 meters to form a physical pendulum. Assuming small amplitude motion, calculate its period of oscillation. For a disk, I = (1/2)MR2 about its center of mass.
The vibration modes and the motion pattern of a bridge system can be foreseen through the application of eigenvalue and eigenvector. The dynamic system of the bridge can be expressed in the matrix form as: а 1 3] A = |1 0 l2 1 1 al where a is the last digit of your matrix number. If the last digit of your number is zero or one then take a = 2. Use try value v = [1 0 1]T and calculate until |mk+1 – mx| < 0.005 or FIVE (5) iterations whichever comes first. Do the calculations in 3 decimal places. Estimate the mode shape of the vibration by finding the dominant (in absolute value) eigenvalue and its motion pattern (corresponding eigenvector). (а)
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(1/15) sec Two strings of same length L are held under the same tension T, and are driven to oscillate at the same frequency f. String A has a linear mass density u and string B has a linear density 4u. If the number of loops on A is n-4, then the number of loops on B is: O 4 O 16 8. A taut string of length 2m is fixed at both ends, and tension is maintained at a
1(a) A damped simple harmonic oscillator has mass 2.0 kg, spring constant 50 N/m, and mechanical resistance 8.0 kg/s. The mass is initially released from rest with displacement 0.30 m from equilibrium. Determine the displacement x(t) as a function of time without assuming weak dissipation. Numerically compute all quantities. (b) The time for transients to become negligible is typically taken to be 5t, where the time constant t is the time required for the amplitude to decay to e-1 of its initial value. Taking the displacement amplitude to be approximately A = 0.30 m, (which holds for weak damping), determine the amplitude at time 5t. = Xoe¬Bt where xo
In the figure, a string, tied to a sinusoidal oscillator at Pand running over a support at Q, is stretched by a block of mass m. Separation L 1.3 m, linear density u= 1.1 g/m, and the oscillator frequency f= 120 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q. %3D %3D (a) What mass m allows the oscillator to set up the fourth harmonic on the string? (b) What standing wave mode, if any, can be set up if m = 1 kg (Give O if the mass cannot set up a standing wave)? %3D Oscillator L- Units (a) Number i Units (b) Number