1. A mass spring system has a mass of 1kg, a damping constant of 7 Ns/m and a springconstant of 10 N/m. The mass is initially sitting at rest at the equilibrium point. Startingat t = 0, an external force of 120N is applied to the mass in the positive direction. (Thatis - the force is stretching the spring) This external force stops at t = 0.5, after whichthere is no external force.a.Write a piecewise-defined formula for the external force Fext (t) as a functionof t. Then calculate its Laplace transform L{Fext (t)} (You will need this later)b.Write the initial value problem describing the situation. You can leave theexternal force written as Fext (t), but understand that it is the piecewise-definedfunction from part a.C.Solve the initial value problem from part a by taking the Laplace transform ofboth sides.

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Answered: 1. A mass spring system has a mass of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. A spring is such that a 4-lb weight stretches the spring 0.40 ft. The 4-lb weight is attached to the spring (suspended from a fixed support) and the system is allowed to reach equilibrium. Then the weight is started from equilibrium position with an imparted upward velocity of 2 ft/sec. Assume that the motion takes place in a medium that furnishes a retarding force of magnitude numerically equal to the speed, in feet per second, of the moving weight. Determine the position of the weight as a function of time. 2. Find the Laplace transform of a) t² sinkt b) tsinkt 3. Find the Inverse Laplace transform of : 5s-2 s² (s+2) (S-1) S b) (s²+²)(s²+b²) a² + b², a²b², ab 0 4. Use the Laplace Transform method to solve the given system dx dy (a) 2x - y = 6e³t, dt dt 2x-3x+ x(0) = 3, d²₂ dy dt² dt dx -x+ dt dx + 3x + - 4y + 3z = 0; dt dx x(0) = 0, (0) = 1, y(0) = 0, z(0) = 0. dt 5. Find the Fourier series to represent a function of a.) f(x) = x + 1, - 2 < x < 0, = 1, 0
Pls answer question 1 part B
A mass weighing 16 lb stretches a spring 1/4 feet. The mass is attached to a viscous damper with a damping constant of 2 lb-s/ft and is set in motion from its equilibrium position with a downward velocity of 1/2 ft/s. a) Set up the initial value problem (differential equation). b) Solve the equation to find the position of the mass y at any time t. c) Determine when the mass first returns to its equilibrium position. Assume that the y-axis is directed downward.
ta If Jane can finish the job in 6 hours while Jenny can finish the same job in 9 hours, how would you represent the time it takes them to finish the job if they work together?
2. A mass that weighs 64 lb stretches a spring 0.8 ft. The mass is attached to a dashpot mechanism that has a damping coefficient of 8 lb s/ft and is acted on by an external force of 60 cos(4t) lb. The mass is set in motion from its equilibrium position with no initial velocity. Let y(t) denote the displacement (in ft) of the mass from its equilibrium position after t seconds. (a) Find an initial-value problem which describes this process. (You may use the fact that g = 32 ft/s' and 1 ft=12 in.) (b) Is the system underdamped, overdamped, or critically damped? Justify your an- swer.
A spring is pulled back 4cm below its equilibrium point and then released. If the spring has a period of 3 seconds, which of the following models the position of this spring after t seconds? Select one: O a. s()– 3sin:) O b. (21 s(?) = - 3cos :) 21 s(t) = - 4sin O d. s(t): = -4cos
NEED FULLY CORRECT HANDWRITTEN SOLUTION FOR THIS..... ASAP!!!!
Find (u, v), |u, vl, and d(u, v) for the given inner product defined on R". u = (-5, 4), v = (0,-2), (u, v) 3u,v, + UZV2 (a) (u, v) (b) (c) (d) (A 'n)p
a) A mass, m = 200N is attached to the free end of a vertical spring as shown in Figure Q3(a), where the damping coefficient, c 10N.s/m and the spring constant, k = 20N/m. When displaced from the equilibrium position, the mass is subjected to free vibration response which can be described by the pendulum motion: d2x m at? dx + kx = 0 dt where x is the horizontal displacement from the equilibrium position and t is time. The displacement (x) as a function of time t is given below, where the initial velocity y(t=0) is zero. + x(t) x (m) 0.005 0.005 0.005 -0.0575 -0.08875 t (s) 10 15 20 Figure Q3(a) i) Assume y = dt' dx reduce the system to first order differential equation. ii) Determine the first order differential equation over the time period of Os t s 20s seconds using the Euler's method. (CO2,PO2)(C3)
4.4 11 11. A 0.2-kg mass is attached to a spring having a spring constant 5 kg/s2. The system is displaced 0.5 m from its equilibrium position and released from rest. If there is no damping present, find the amplitude, frequency, and phase of the resulting motion. Plot the solution.

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