A phase-time plot stacks a pendulum's states (θ, ω) up a time axis, so each swing is one turn of a curve, not a loop retraced. Here θ″ = −(g/L) sin θ − 2cθ′, L = 1.7 m, c = 0.15 s⁻¹, from rest at 1 rad. The swing shrinks as e^(−ct), losing 95 % of its energy in 10 s, so the

Name: A phase-time plot stacks a pendulum's states (θ, ω) up a time axis, so each swing is one turn of a curve, not a loop retraced. Here θ″ = −(g/L) sin θ − 2cθ′, L = 1.7 m, c = 0.15 s⁻¹, from rest at 1 rad. The swing shrinks as e^(−ct), losing 95 % of its energy in 10 s, so the
Channel: matharium
Description: A phase-time plot stacks a pendulum's states (θ, ω) up a time axis, so each swing is one turn of a curve, not a loop retraced. Here θ″ = −(g/L) sin θ − 2cθ′, L = 1.7 m, c = 0.15 s⁻¹, from rest at 1 rad. The swing shrinks as e^(−ct), losing 95 % of its energy in 10 s, so the

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A phase-time plot stacks a pendulum's states (θ, ω) up a time axis, so each swing is one turn of a curve, not a loop retraced. Here θ″ = −(g/L) sin θ − 2cθ′, L = 1.7 m, c = 0.15 s⁻¹, from rest at 1 rad. The swing shrinks as e^(−ct), losing 95 % of its energy in 10 s, so the

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