A circular disk suspended by a thin wire attached to the center of one of its flat faces is twisted through an angle θ. Torsion in the wire tends to turn the disk back in the opposite direction (thus, the name torsion pendulum is given to this device). The angular displacement θ (in rad) as a function of time t (in s) is θ = θ₀ cos(ωt + ∅), where θ₀  is the maximum angular displacement, θ is a constant that depends on the properties of the disk and wire, and ∅ is the phase angle. Sketch the graph of θ vs. t if θ₀ = 0.100 rad, ω = 2.50 rad/s, and ∅ = π/4. See Fig. 10.50.

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Fig. 10.50 -0