3) Consider a one-dimensional flow with velocity u(x,t) satisfying the equation Ut + uug (This corresponds...

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3) Consider a one-dimensional flow with velocity u(x,t) satisfying the equation Ut + uug (This corresponds to an "elastic" medium with a restoring force that pushes each particle back to the origin) and the initial condition u(x, 0) = uo(x). What is the position x at time t of a particle that starts at position x = x0 at time t = 0? (Hint: write down the characteristic equations for u and x, solve them -think sines and cosines- and fit the initial data.) 3) Consider a one-dimensional flow with velocity u(x,t) satisfying the equation Ut + uug (This corresponds to an "elastic" medium with a restoring force that pushes each particle back to the origin) and the initial condition u(x, 0) = uo(x). What is the position x at time t of a particle that starts at position x = x0 at time t = 0? (Hint: write down the characteristic equations for u and x, solve them -think sines and cosines- and fit the initial data.)