At time t 0 the particle is projected from the point x 1, Mechanical Engineering

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At time t 0 the particle is projected from the point x 1

An overdamped harmonic oscillator satisfies the equation

x^·· + 10x^· + 16x =0.

At time t = 0 the particle is projected from the point x = 1 towards the origin with speed u. Find x in the subsequent motion. Show that the particle will reach the origin at some later time t if

(u-2)/(u-8) = e^6t.

How large must u be so that the particle will pass through the origin?

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Mechanical Engineering: At time t 0 the particle is projected from the point x 1

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Mechanical Engineering: At time t 0 the particle is projected from the point x 1

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