Art core problems

Problem 1 – Resonant color mixing#

A painter uses three pigment emitters aligned with $$D_3$$, each oscillating at frequencies $$f_1, f_2, f_3$$. When elevated by $$T_f$$, the composite color resonance is

$$ C = X(f_1 + f_2 + f_3), \quad X = F_3 \cdot T_f. $$

If the painter wants to double the perceived saturation by adjusting resonant-time $$τ_r$$, and saturation is proportional to $$C$$, by what factor must $$τ_r$$ be scaled?

Problem 2 – Sculpture stress harmonics#

A kinetic sculpture rotates with a triadic stress pattern governed by

$$ S = D_6(τ_r) \cdot ΛΘ. $$

If the artist increases the temperature constant $$Θ$$ by 20%, how does the sculpture’s harmonic stress $$S$$ change, assuming all other parameters remain fixed?

Problem 3 – Light installation timing#

A gallery installation uses pulsed LEDs whose brightness cycles follow

$$ B(t) = F_3 \sin(T_f t). $$

The artist wants the brightness to peak exactly every 4 seconds. The effective elevated frequency is $$T_f' = T_f / τ_r$$. What value of $$τ_r$$ is required to achieve a 4-second peak period?