For the following, use the spring equation:e dy k+m dt mdt²+with c = 4, mues of k:1. k=5(b)(c)-y01, and the initial conditions: y(0) = 2 and y'(0) = 0. For each of the following val-Find the general solution.Find the solution for these initial values.Sketch the timeplot graph of the solution y(t). In terms of the spring, is it underdamped,critically damped, or overdamped?

Given Data: d2ydt2+cmdydt+kmy=0 c=4, m=1initial conditionsy(0)=2 and y'(0)=0k=5 Find: (a) Find the…

For the following, use the spring equation: d'y e dy + dt² m dt +-y=0 TIL with c 4, m 1, and the initial conditions: y(0) ues of k: 1. k=5 (a) (b) 2 and y'(0) Find the general solution. Find the solution for these initial values. -0. For each of the following val- Sketch the timeplot graph of the solution y(t). In terms of the spring, is it underdamped, critically damped, or overdamped?

For the following, use the spring equation: d'y e dy + dt² m dt +-y=0 TIL with c 4, m 1, and the initial conditions: y(0) ues of k: 1. k=5 (a) (b) 2 and y'(0) Find the general solution. Find the solution for these initial values. -0. For each of the following val- Sketch the timeplot graph of the solution y(t). In terms of the spring, is it underdamped, critically damped, or overdamped?

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

My question and answer is in the image. Can you please check my work? A 2 kg mass is attached to a spring with spring constant 50 N/m. The mass is driven by an external force equal tof(t) = 2 sin(5t). The mass is initially released from rest from a point 1 m below the equilibrium position. (Use theconvention that displacements measured below the equilibrium position are positive.)(a) Write the initial-value problem which describes the position of the mass. 2y"+50y=2cos(5t) (b) Find the solution to your initial-value problem from part (a). (1+(1/2)tcos(t))cos(5t)-(1/2)tcos(t) (c) Circle the letter of the graph below that could correspond to the solution. B (d) What is the name for the phenomena this system displays? Resonance
A mass spring system has a mass of 3/4 kg, a damping constant of 3/2 kg/sec and a spring constant of 15/2 kg/sec. There is no external force. The system is started in motion at y = 4 meters with an initial velocity of 3 m/s in the downward direction. a) Find the differential equation and the initial conditions that describe the motion of this system. b) Solve the resulting initial value problem. c) Is the spring system overdamped, underdamped or critically damped?
A force of 20 newton stretches a spring 1 meter. A 5 kg mass is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 10 times the instantaneous velocity. (a) Let x denote the downward displacement of the mass from its equilibrium position. [Note that x>0 when the mass is below the equilibrium position. ] Assume the mass is initially released from rest from a point 3 meters above the equilibrium position. Write the differential equation and the initial conditions for the function x(t)(b) Solve the initial value problem that you wrote above.(c) Find the exact time at which the mass passes through the equilibrium position for the first time heading downward. (Do not approximate.)(d) Find the exact time at which the mass reaches the lowest position. The "lowest position" means the largest value of x
you are given the mass, damping, andspring constants of an undriven spring-mass systemmy'' + μy + ky = 0.You are also given initial conditions. Use a numerical solverto(i) provide separate plots of the position versus time (y vs.t) and the velocity versus time (v vs. t),(ii) provide a combined plot of both position and velocity versus time, and(iii) provide a plot of the velocity versus position (v vs. y) inthe yv phase plane. a. m = 1 kg, μ = 0 kg/s, k = 9 kg/s2, y(0) = 3 m,y'(0) = 2 m/s b.m = 4 kg, μ = 4 kg/s, k = 1 kg/s2, y(0) = 3 m,y'(0) = 1 m/s
A driven damped oscillator has k = 32.0 N/m, m = 0.5 kg and b = 1Ns/m. If F(t)=F0 cos ωt with F0 = 10N is the oscillator's driving force and ω= 2ω0 where ω0 is its natural frequency. Solve for the initial conditions x(t=0) = 2m and v(t=0) = 0 using a differential equation method.
which equation is used if the system underdamped. can you pls share the whole eqn
A long spring has a mass of 1 slug attached to it. The spring stretches 16/13 ft and comes to rest. The damping coefficient is 2 slug/s. The mass is subjected to an impulsive force at time t = 0, which imparts a velocity of 5 ft/s downward. set up the differential equation that describes the motion. Solve the differential equation. State whether the motion of the spring-mass system is harmonic, damped oscillation, critically damped, or overdamped.
laplace transform
Determine the fundamental natural frequency of the spring mass system shown in Fig.1 using (i) Dunkerley’s method and (ii) Matrix iteration method (only 2 iterations).
A force of 20 newton stretches a spring 1 meter. A 5 kg mass is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 10 times the instantaneous velocity. 1) Let x denote the downward displacement of the mass from its equilibrium position. [Note that x>0 when the mass is below the equilibrium position. ] Assume the mass is initially released from rest from a point 3 meters above the equilibrium position. Write the differential equation and the initial conditions for the function x(t) 2) Solve the initial value problem that you wrote above. 3)Find the exact time at which the mass passes through the equilibrium position for the first time heading downward. (Do not approximate.) 4)Find the exact time at which the mass reaches the lowest position. The "lowest position" means the largest value of x
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.
Solve the following initial value problem by the method of Laplace Transform