WS01 - APPM 4/5350 Worksheet Week 1 Figure 1: www.xkcd.com...

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APPM 4/5350 Worksheet Week 1 Figure 1: www.xkcd.com 1. ODEs (a) Find a solution θ ( t ) for: m ¨ θ = - g sin( θ ) with small angle approximation sin( θ ) θ , and initial conditions θ (0) = 0 , ˙ θ (0) = 1 (b) Obtain a general solution y ( t ) (including arbitrary constants) for y 0 + βty = 1 β = const 2. Equilibrium Solution Find the general equilibrium solution (including arbitrary constants) for: 2 g ∂t 2 = 2 g ∂x 2 - αg, α > 0 What does it mean to have an equilibrium solution and given g ( x,t ) how would one find the equilibrium behavior if it exists.
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