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Engineering · Mechanical Engineering
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11-Consider the equation describing the small angular displacement θ,of a pendulum in a viscous liquid. A force balance gives wherew > 0. The term σ de is damping due to friction within the liquid. dt (a) Make the equation dimensionless by defining at to show that the (10%) solution θ(t) depend on a single dimensionless parameter β (b)Find the equation θ(t) and θ(r) for β 1 and β# 3 for the homogeneous equation when there is no force, L.e.f(t) 0, with the boundary conditions θ(0)s θο, θ.0. (10%) (c) Find the general solution θ(r) for β-1 when there is a decaying forcing f(t)-e-set where ω is real constant. (10%)
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