The pendulum vibrates with an amplitude of 10 mm and a frequency of 2 Hz. What is the maximum speed of the pendulum?

The pendulum oscillates and its coordinate x changes depending on the change in time t according to the law x = x₀ ∙ sin ω ∙ t, where x₀ is the amplitude of the pendulum’s oscillations, ω is the cyclic frequency. The cyclic frequency is determined by the formula ω = 2 ∙ π ∙ ν, where ν is the oscillation frequency of the pendulum. Then the oscillation speed of the pendulum v will vary according to the law v = (x₀ ∙ sin ω ∙ t) ‘= x₀ ∙ ω ∙ cos ω ∙ t = v₀ ∙ cos ω ∙ t, where v₀ = x₀ ∙ ω = 2 ∙ x₀ ∙ π ∙ ν is the maximum speed of the pendulum. From the condition of the problem it is known that the amplitude of the pendulum’s oscillations is x₀ = 10 mm = 0.01 m, the oscillation frequency of the pendulum is ν = 2 Hz, then:
v₀ = 2 ∙ 0.01 ∙ π ∙ 2;
v₀ = 0.04 ∙ π ≈ 0.1256 (m / s).
Answer: the maximum speed of the pendulum is ≈ 0.1256 m / s.