MATH 307 Midterm: MATH 307 UW 307 Su10 Sol2

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turquoisegnu128

31 Jan 2019

School

Department

Mathematics

Course

MATH 307

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All

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Document Summary

Math 307, sections a and b, summer 2009, solutions to midterm ii: a force of 2. 5 newtons stretches a spring 40 cm. A mass of 2 kg is attached to the spring and an external force of 4cos(t) newtons acts on the mass. The system is placed in a liquid that imparts a viscous force of 2 newtons when the speed is 2 meters per second. The mass is set in motion from the equilibrium position with an initial velocity if 4 cm/sec. (14 points) (a) formulate the initial value problem for the position of the mass as a function of time. m = 2. 2u + u + 6. 25u = 4 cos t, u(0) = 0, u (0) = 0. 04. (b) find the steady state solution. (how does the solution behave when t is very large?) U (t) = a cos t + b sin t,

Related Questions

can you solve this please

Trying to solve this Differential equations problem:
A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to f(t) = sin(4t) is applied to the system. The surrounding medium offers a damping force numerically equal to 8 times the instantaneous velocity. The equation of motion satisfies the initial-value problem

x'' + 8x' + 16x = sin(4t), x(0) = 0, x'(0) = 0. Find the equation of motion.

Please show work so Ican walk through it!