Engineering core problems

Problem 1 – Structural resonance load#

A beam’s resonant load is modeled as

$$ L = \frac{D_6}{τ_r}. $$

If $$τ_r$$ doubles, what happens to the load $$L$$?

Problem 2 – Thermal expansion under resonance#

Thermal expansion of a material is modeled as

$$ E = ΛΘ T_f. $$

If $$Θ$$ increases by 15% and $$T_f$$ decreases by 5%, what is the net percent change in $$E$$?

Problem 3 – Fluid flow resonance#

A fluid flow rate under resonance is

$$ Q = F_3 τ_r^2. $$

If $$τ_r$$ increases by 10%, what is the percent increase in $$Q$$?