Engineers can determine properties of a structure that is modeled as a damped spring oscillator, such as a bridge, by applying a driving force to it. A weakly damped spring oscillator of mass 0.245 kg is driven by a sinusoidal force at the oscillator's resonance frequency of 30.2 Hz. Find the value of the spring constant k. k= N/m The amplitude of the driving force is 0.424 N and the amplitude of the oscillator's steady-state motion in response to this driving force is 0.898 m. What is the oscillator's damping constant b? b = kg/s

Engineers can determine properties of a structure that is modeled as a damped spring oscillator, such as a bridge, by applying a driving force to it. A weakly damped spring oscillator of mass 0.245 kg is driven by a sinusoidal force at the oscillator's resonance frequency of 30.2 Hz. Find the value of the spring constant k. k= N/m The amplitude of the driving force is 0.424 N and the amplitude of the oscillator's steady-state motion in response to this driving force is 0.898 m. What is the oscillator's damping constant b? b = kg/s

Name: Engineers can determine properties of a structure that is modeled as
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: Engineers can determine properties of a structure that is modeled as a damped spring oscillator, such as a bridge, by applying adriving force to it. A weakly damped spring oscillator of mass 0.245 kg is driven by a sinusoidal force at the oscillator

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 47P

See similar textbooks

Similar questions

Which of the following statements is not true regarding a massspring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
A 200-g block is attached to a horizontal spring and executes simple harmonic motion with a period of 0.250 s. The total energy of the system is 2.00 J. Find (a) the force constant of the spring and (b) the amplitude of the motion.
A spherical bob of mass m and radius R is suspended from a fixed point by a rigid rod of negligible mass whose length from the point of support to the center of the bob is L (Fig. P16.75). Find the period of small oscillation. N The frequency of a physical pendulum comprising a nonuniform rod of mass 1.25 kg pivoted at one end is observed to be 0.667 Hz. The center of mass of the rod is 40.0 cm below the pivot point. What is the rotational inertia of the pendulum around its pivot point?
For a damped, driven oscillator, show that the average kinetic energy is the same at a frequency of a given number of octaves* above the kinetic energy resonance as at a frequency of the same number of octaves below resonance.
Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = bv2 and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, E=12mv2+12kx2, and use Equation 15.51.
A 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.
An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
If the amplitude of a damped oscillator decreases to 1/e of its initial value after n periods, show that the frequency of the oscillator must be approximately [1 − (8π2n2)−1] times the frequency of the corresponding undamped oscillator.
A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension (Fig. P15.55). Find the frequency of vibration of the system for small values of the amplitude (small ). Assume the vertical suspension rod of length L is rigid, but ignore its mass. Figure P15.35
Plot a velocity resonance curve for a driven, damped oscillator with Q = 6, and show that the full width of the curve between the points corresponding to is approximately equal to ω0/6.
Consider the system shown in Figure P16.68 as viewed from above. A block of mass m rests on a frictionless, horizontal surface and is attached to two elastic cords, each of length L. At the equilibrium configuration, shown by the dashed line, the cords both have tension FT. The mass is displaced a small amount as shown in the figure and released. Show that the net force on the mass is similar to the spring-restoring force and find the angular frequency of oscillation, assuming the mass behaves as a simple harmonic oscillator. You can assume the displacement is small enough to produce negligible change in the tension and length of the cords. FIGURE P16.68