Simple harmonic motion: spring, mass, sine wave
A block attached to a spring oscillates back and forth while its position x(t) = A cos(omega t) is traced live on a graph beside it. The animation links the physical motion to the equation, showing why speed peaks at the equilibrium point and drops to zero at the endpoints. Formulas for restoring force F = -kx, angular frequency omega = sqrt(k/m), and period T = 2 pi / omega are displayed alongside the motion, making the connection between force, mass, stiffness, and timing clear for introductory physics students.
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The prompt that made it
A mass on a spring oscillates while x(t) = A cos(omega t) is traced on a graph in sync; F = -kx, omega = sqrt(k/m), T = 2 pi / omega; slowest at the ends, fastest through the middle.
Make the next one in this series
- Show how amplitude and phase shift change the x(t) graph and the spring's motion.
- Animate the energy exchange between kinetic and potential energy during one oscillation cycle.
- Compare a simple pendulum's motion side by side with the spring-mass system's equations.
