Consider a mass - spring - damper system with mass of 3, damping constant 6, and spring constant 12, and an external force of r(t) = 3 cos(wt). (a) Find the value of w that will result in the largest amplitudes in the steady state of the system. (b) Using your value of w from part a), find a function to describe the displacement of the system as a function of time, if the initial displacement is 1, and the initial velocity is 0. (c) Suppose the external force of r(t) equilibrium position (so it has 0 displacement and 0 velocity), and an instantaneous force is applied, given by r(t) = 38(t – 2). Find a function that describes the displacement of the system as a function of time with this new input. 3 cos(wt) is then stopped, the system is returned to its

Consider a mass - spring - damper system with mass of 3, damping constant 6, and spring constant 12, and an external force of r(t) = 3 cos(wt). (a) Find the value of w that will result in the largest amplitudes in the steady state of the system. (b) Using your value of w from part a), find a function to describe the displacement of the system as a function of time, if the initial displacement is 1, and the initial velocity is 0. (c) Suppose the external force of r(t) equilibrium position (so it has 0 displacement and 0 velocity), and an instantaneous force is applied, given by r(t) = 38(t – 2). Find a function that describes the displacement of the system as a function of time with this new input. 3 cos(wt) is then stopped, the system is returned to its

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

Suppose a spring with spring constant 7 N/m is horizontal and has one end attached to a wall and the other end attached to a 2 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N⋅s/m a) Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x,x′,x′′. Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. b) Find the general solution to your differential equation from the previous part. Use c1 and c2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Your answer should be an equation of the form x=… c) Enter a value for the damping constant that would make the system critically damped. ?Ns/m
A spring-mass system with m = 0.5 kg and k = 10,000 N/m, with negligible damping, is used as a vibration pickup. When mounted on a structure vibrating with an amplitude of 4 mm, the total displacement of the mass of the pickup is observed to be 12 mm. Find the frequency of the vibrating structure.
The mass of a spring-mass system, with m = 12 kg and k = 35 kN/m, vibrates on a horizontal surface under a harmonic force of magnitude 300 and a frequency of 19 Hz. Find the resulting amplitude of steady state vibration. Assumethe coefficient of friction between the mass and the horizontal surface as 0.25
A vibrating system with mass 3 kg, stiffness 21 N-s/m and damper having damping coefficient 10 N-s/m When an exciting force of magnitude 27 sin2t is acting, what would be the time period of oscillations?
For a system with mass 10 kg, spring constant 100 N/m, damping ratio 1 kg/s, rotating unbalance of 0.1 kg, radius 100 cm, and driving frequency 50 Hz, what is the amplitude of the particular solution? What is the phase lag of the particular solution?
A vibrating system has the following parameters: m = 18 kg, K = 70 N / cm,c = 0.8 N.s / cm. Determine: a) The damping factor ξ, b) The frequency ofdamped oscillation ωD, c) the logarithmic decrease, d) the ratio of two amplitudes any consecutive and e) The equation of the general position X (t)
A spring-mass-damper system oscillating about the horizontal surface is subjected to anexternal force of F = 300 sin (6)(t), where 300 is in Newtons and 6 is in radians per second. Thesystem has a mass 90 [kg], a damping coefficient of 78 [N ⋅ s/m] and a spring constant of300 [N⁄m]. The system is both given an initial displacement of 1.2 [m] and an initial velocity of 1.4[m⁄s].a. Using Method of Undetermined Coefficients, determine the particular solution for thedisplacement function.b. Determine the unknown coefficients for the homogeneous solution using the initialconditions (Note: the external force already works at t = 0).c. Determine the position, velocity, and acceleration of the system after 10 seconds.
A heavy machine, weighing 3000 N, is supported on a resilient foundation. The static deflection of the foundation due to the weight of the machine is found to be 7.5 cm. It is observed that the machine vibrates with an amplitude of 1 cm when the base of the foundation is subjected to harmonic oscillation at the undamped natural frequency of the system with an amplitude of 0.25 cm. Find a. the damping constant of the foundation, b. the dynamic force amplitude on the base, and c. the amplitude of the displacement of the machine relative to the base.
A suspension system of Volvo articulated dump truck is to be modelled mathematically given the following data: keq = 10.5 MN/m, m = 30 tons, and c = 300 N-s/m. If the harmonic forcing function is 2000 cos 5t N with the initial displacement and velocity to be 0 and 30 m/s respectively, determine the steady state and total response of the system.
Two mass-spring systems are experiencing damped harmonic motion, both at 0.7 cycles per second and both with an initial maximum displacement of 12 cm. The first has a damping constant of 0.6, and the second has a damping constant of 0.2. a. Find functions of the form to model the motion in each case. b. How do they differ? (Hint: graph the two functions)
In the figure, a disk-shaped wheel of mass M and radius R rolls without slipping on a circular platform of radius 2L+R. The wheel is attached by a torsion spring to a pendulum of length 2L of mass m and moves with this pendulum.a) Derive the differential equation for the motion of the system given here.b) Find the natural frequency of the free motion of the system. L=2 [m], R= 0,5 [m], m=5 [kg], M= 65[kg], kb= 165 [Nm/rad] Note: There is no friction in this system
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.