11. In the spring-mass-damper system shown in the diagram below, the mass is regarded to be negligibly small. The system is disturbed by an external force which leads to the simplified first degree differential equation d+ y =!1 where n is the damping constant and k the spring constant and y is the displacement of the mass dtn from its equilibrium. Solve this differential equation if it is known that y(0) = 0. Present your solution with y as the subject. Determine the steady state of y. Hint: Since k and n are constants, let = M and != N, that is, solve + My = Nt. dt Dinube Spag Deper

11. In the spring-mass-damper system shown in the diagram below, the mass is regarded to be negligibly small. The system is disturbed by an external force which leads to the simplified first degree differential equation d+ y =!1 where n is the damping constant and k the spring constant and y is the displacement of the mass dtn from its equilibrium. Solve this differential equation if it is known that y(0) = 0. Present your solution with y as the subject. Determine the steady state of y. Hint: Since k and n are constants, let = M and != N, that is, solve + My = Nt. dt Dinube Spag Deper

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

using differential equation A mass weighing 2.45N stretches a spring 0.6125 meter. Assuming that a damping force numerically equal to 2 times the instantaneous velocity acts on the system, Determine the equation of motion if the mass is initially released from the equilibrium position with an upward velocity of 3 m/s. What is the position of the mass when t= 1/4 sec.
Differential equations When a mass of 2 kilograms is attached to a spring whose constant is 32N/m, it reaches rest in the equilibrium position. Starting at t = 0, a force equal to f(t) =68e-2tcos(4t) is applied to the system. Determine the equation of motion in the absence of damping. Pls dont skip steps 68e-2tcos(4t)
A mass weighing 5 pounds is attached to a spring whose constant is k = 7lb/tf. The medium offers a damping force that is foot numerically equal to the instantaneous velocity. The mass is released from a point 1 ft above the equilibrium position with a downward velocity of 8 ft/seg. Determine the equation of motion x(t) of this system
A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine the equations of motion if the following is true. (Show a sketch of the problem) (a) the mass is initially released from rest from a point 1 meter below the equilibrium position (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s (c) In parts a and b of the problem, determine whether the mass passes through the equilibrium position. In each case find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant?
Two blocks A and B, each of mass m , are supported as shown by three springs of the same constant k Block A and B are connected by a dashpot and block B is connected to the ground by two dashpots, each dashpot having the same coefficient of damping c Block A is subjected to a force of magnitude P=Pm sin wf t. Write the differential equations defining the displacements xA and xB of the two blocks from their equilibrium positions.
A vibration system with a single degree of freedom has a spring stiffness of 7613.3 N/m, a mass of 55 kg, and a critical damping of 1.26x103 N.s/m. If the system's starting velocity is 2 m/s. Determine the system's displacement and velocity after two seconds.
The equivalent mass of a SDOF of 10 kg. The system has a natural frequency of 80 rad/s. The system is at rest in equilibrium when it is subject to a time dependent force. Determine and plot the response of the system if it is subject to a force of (a) 10 sin(40t)N, (b) 10 sin(80t) N, and (c) 10 sin(82t) N.
A mass-spring-damper system has a l0ad 0f 2 kg, a spring c0nstant 0f 8 N/m, and a damping c0efficient 0f 8 N/s.m. The system is initially in equilibrium. At t=0, the mass is given an initial vel0city 0f 3 m/s d0wnwards. Determine the p0sition vs time (t) of the l0ad. Is the system underdamped, 0verdamped, 0r critically damped?
The equation of motion of a certain mass-spring-damper system is 5x'' + cx' +10x = f(t). Suppose that f(t) = Fsin(wt). Define the magnitude ratio as M = X/F. Determine the natural frequency w_n, the peak frequency w_p, and the peak magnitude ratio M_p for damping ratio = 0.1 and the damping ratio = 0.3
The amplitude of vibration of a single degree of freedom spring-mass-damper system is observed to reduce to 15 % of its initial value after 5 cycles. Spring stiffness equals (1509N/m and mass equals (16.5 kg. Determine: The undamped natural frequency; The damped natural frequency; The logarithmic decrement; The damping ratio; and The coefficient of damping.
A 64-lb weight suspended from a spring (spring constant is 200 lb/ft) is released from rest 0.4 ft below the equilibrium position. If there is a resistance (lb) numerically equal to 0.04 times the velocity at any instant, determine the time for the damping factor to decrease 50% of its initial value g=32 ft/sec square
An oscillator system without damping has a natural frequency of omega 0 = pi rad/s. Several types of attenuation are given to the system to provide a damping factor (y) of 0.1, 0.5 and 1 s^-1. (a) For each damping factor value, determine the omega value of the oscillator!. (b) determine the displacement at time t = 2 seconds for the damping factor y = 0.5 , if the displacement at t = O is 30 mm and v = 1.5 m/s