⚡ Damped Oscillator Simulator

Analyze classical mass-spring-damper dynamics ($m\ddot{x} + c\dot{x} + kx = F_0\cos\omega t$). Inspect damping ratios ($\zeta$), Q-factor resonance peaks, phase lag, and transient vs steady-state response.

Mass ($m$) kg

Spring Stiffness ($k$) N/m

Damping ($c$) N·s/m

Driving Freq ($\omega$) rad/s

Spring-Mass-Dashpot

Magnification $M(\beta)$ vs $\beta = \omega/\omega_n$

Natural Freq ($\omega_n$)

10.0 rad/s

1.59 Hz

Damping Ratio ($\zeta$)

0.100

UNDERDAMPED

Dynamic Amplification ($M$)

5.00×

Quality Factor Q = 5.0

Phase Lag ($\phi$)

90.0°

Freq ratio $\beta = 1.00$