Harmonic Oscillator & Phase Space Explorer

x(t) = A cos(ωt + φ)
Drag Mass or Phasor Vector directly to perturb state
Physical Parameters Active
Mass (m) 1.00 kg
Spring Constant (k) 4.00 N/m
Damping Ratio (γ) 0.00 s⁻¹
Derived State & Kinematics
Angular Frequency (ω) 2.00 rad/s
Natural Period (T) 3.14 s
Position x(t) 1.06 m
Velocity v(t) -2.12 m/s
Trajectory Classification closed_ellipse
Mechanical Energy Partition
Kinetic (E_k)
0.00 J
Potential (E_p)
0.00 J
Total (E_tot)
4.50 J

Demonstrates continuous phase shift energy balance: Total energy $E = \frac{1}{2}kA^2$ transfers losslessly between elastic potential and kinetic states under zero damping ($\gamma = 0$).

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