Physics
3D oscillator systems
Mass-spring cubes, membranes and chains, plus sixteen exact modes of a fixed square membrane. Strike a point, excite a mode or drive a resonance.
What happens
Masses and springs assembled into 3D bodies: a jelly cube that wobbles when dropped, a membrane that rings like a drumhead when plucked, a hanging chain. Soften the stiffness and the cube turns to pudding; the energy chart watches the oscillations breathe and slowly die into damping.
Equations used in the module
Equations m r_i'' = Σ_j k(l_ij−L_ij)(r_j−r_i)/l_ij + mg − mγr_i' Kφ = ω²Mφ; h ω_max < 2 v_(n+½) = v_n + ½h a_n; r_(n+1) = r_n + h v_(n+½) f_mn = (1/2L)√(T/μ)√(m²+n²) u(x,z,t) = Σ q_mn(t) sin(mπx/L) sin(nπz/L)
