A spring-mounted payload rides above a shaker base with a transparent viscous damper. You compare free decay with base excitation, change damping and stiffness, and observe relative motion and the energy dissipated as heat.
• A suspended payload, helical spring, viscous dashpot cutaway, electrodynamic shaker base, and energy and phase indicators. • Controls for excitation (release from displacement or sinusoidal base motion), payload mass (1-10 kg), spring stiffness (100-1000 N/m), viscous damping (0-100 N·s/m) and base frequency (0.5-5 Hz). • Readouts of absolute payload displacement, spring/damper relative deflection, damping ratio ζ, undamped natural frequency, mechanical energy and cumulative damper dissipation. • Experiments: undamped free oscillation, strongly damped release, and driving near resonance.
The equation is m ẍ + c(ẋ − ẏ) + k(x − y) = 0. Free decay starts from x(0) = 0.04 m with y = 0; base excitation uses y = 0.01 sin(2πft). The natural frequency is fn = √(k/m)/(2π), ζ = c/(2√km), E = ½mv² + ½k(x − y)², and heat = ∫c(v − ẏ)² dt, advanced with a fixed-step RK4 integrator.
This is a linear single-degree-of-freedom viscous model around static equilibrium with exaggerated visual displacement. It has no dry friction, nonlinear spring limits, material fatigue or damper heating feedback. Base excitation supplies energy, so mechanical energy plus heat is not conserved in that mode.
No. Dissipated power is damping times relative velocity squared.
No. The moving base performs work on the system, so mechanical energy plus heat is not conserved in that mode.
Near the natural frequency, low damping allows large motion; the lab lets you compare it with higher damping.
fn = √(k/m)/(2π) and ζ = c/(2√km), where m is payload mass, k is spring stiffness and c is viscous damping.