A mass m is accelerated by a time-varying force exp(-ßt)v², where v is its velocity. It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore dv m - dt - exp(-ßt)v³ – nv. Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity vo.
A mass m is accelerated by a time-varying force exp(-ßt)v², where v is its velocity. It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore dv m - dt - exp(-ßt)v³ – nv. Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity vo.
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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