As a pendulum swings (see the diagram), let t measure the time since it was vertical. The angle θ = θ(t) from the vertical can be shown to satisfy the equation θʹʹ + kθ = 0, provided that θ is small. If the maximal angle is θ = 0.05 radians, find θ(f) in terms of k. If the period is 0.5 seconds, find k. [Assume that θ = 0 when t = 0.]