A spring with the Hooke's law constant k = 1 kg/s² has an oscillating object of mass 4kg attached to it. There is an external force F(t) = cos(wot) applied to the object and no damping force. Find the frequency wo of the external force F(t) which would yield a resonance, that is determine wo for which the equation the amplitude of the moving object increases without bound.

A spring with the Hooke's law constant k = 1 kg/s² has an oscillating object of mass 4kg attached to it. There is an external force F(t) = cos(wot) applied to the object and no damping force. Find the frequency wo of the external force F(t) which would yield a resonance, that is determine wo for which the equation the amplitude of the moving object increases without bound.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Determine the equation of motion of the system in terms of the angle θ using the principle of virtual work. Assume the displacements are small. Determine the characteristic frequency of the structure?Determine the relative damping factor for the structure?
Given an oscillator of mass 2.0kg and spring constant of 180N/m, what is the period without damping? Use numerical methods to model this oscillator with an additional friction force equal to where c is a positive damping constant. Using c=5.0, what is the new period of oscillation. What about for c=10? Assume initial position is 0.2m and initial velocity is zero. Please find the period using the position versus time plot and use the first full cycle of the motion.
2) If the under-damped spring mass system shown at right is CON subject to the force F(t)= Fe (is the radial frequency of excitation), find the steady-state response of the system by the method of Laplace transformation. k2 m FO k/2
A block of mass m hangs from a spring with a spring constant k. The block is initially held so that the spring is unstretched. If the natural circular frequency of the system is 10 radians/sec, how many cycles of vibration will the block experience in five seconds after it is released?
A mass of m = 12 kg is suspended by a spring of stiffness of S = 1 KN/m from a fixedsupport. The mass vibrates freely with amplitude of 0.008 m. Ignore the effect of dampingand mass of the spring. Calculatei. The maximum restoring force.ii. The natural frequency.
A mass weighing 1/4 kg. is attached to a spring with stiffness k = 16 N/m. The mass is displaced 1/2 m. to the right of the equilibrium position and given a rightward velocity of 1 m/sec. Neglect damping and external forces. Find y(t), A, phi, omega, the period P and the first time (t>0) the mass passes through equilibrium.
2. An auxiliary system consisting of a block of mass m2, is connected to the primary system shown in the figure below by a spring of stiffness k2 ,. The auxiliary system can be used as a vibration absorber if the parameters k2, and m2, are chosen correctly. Show that if k2 = w m2 then the steady-state amplitude of the primary system is zero. F, sin ut
O O O O O Clear selection A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with an amplitude A=0.1 m. At what position (x=?) would the kinetic energy of the system be equal to three times its elastic potential energy (K = 3U)? O At x = +0,025 m O At x = +0.1 m O At x = +0.08 m O At x = +0.04 m At x = +0.05 m A block of mass m = 5 Kg is attached to a spring of spring constant k. The block oscillates in simple harmonic motion on a frictionless horizontal surface. The
- A (50 kg) mass is hanging from a spring of stiffness (5 *10ª N/m). A harmonic force has magnitude (100 N) and frequency (100 rad/s) is applied to the system. Determine the following: a) The Amplitude of the forced response if the c. b) The natural frequency of the system.
A mass is suspended from a spring and is pulled down 3 cm from equilibrium and released. It completes a period in 2 seconds. Ignoring damping factors, find the function for the displacement from equilibrium h(t) in centimeters t seconds after the mass is released.
Find the response of a damped spring-mass system when a force F(t), as shown in Figure, acts on the mass m. Assume k = 2500 N/m, c= 10 N-s/m, m = 0.25 kg, T= 2 sec and consider first three harmonics. F(1) +1 2r Time t Figure