Damped Harmonic Oscillator Dataset

This dataset contains time series data generated by a damped harmonic oscillator. The oscillator has a mass of 1 kg, a spring constant of 1 N/m, and a damping coefficient of 0.1 Ns/m. The oscillator is initially displaced by 1 meter and given an initial velocity of 0. The time series data includes the displacement, velocity, acceleration, and power of the oscillator over time.

**Note that this is a constrained dataset: the energy is decreasing through time; the rate of dissipation of energy is the same through time.**

The equation of motion for a harmonic oscillator is given by a 2nd order ODE $$m \dfrac{d^2x}{dt^2}+c \dfrac{dx}{dt}+kx=0$$

where m is the mass of the oscillator, c is the damping coefficient, k is the spring constant, x is the displacement of the oscillator from its equilibrium position, and t is time.

The goal is to predict the evolution of the variables of the system through time. There are data available to evaluate the adjusted model at 3 tasks:
-reconstruction: evaluate the performance at predicting the same time steps used for training;
-extrapolation: evaluate the performance at predicting for a longer time horizon than the one used for training;
-completion: evaluate the performance at predicting different sampled time steps in the same interval as the training.

本数据集收录了由阻尼简谐振子生成的时序数据。该振子的质量为1千克，弹簧刚度系数为1牛顿每米，阻尼系数为0.1牛顿·秒每米。振子初始位移为1米，初始速度为0。时序数据包括振子随时间变化的位移、速度、加速度和功率。请注意，这是一个受限数据集：能量随时间递减；能量耗散率随时间保持恒定。简谐振子的运动方程由二阶常微分方程给出：$$m dfrac{d^2x}{dt^2}+c dfrac{dx}{dt}+kx=0$$其中，m为振子的质量，c为阻尼系数，k为弹簧刚度系数，x为振子相对于平衡位置的位移，t为时间。研究目标是预测系统变量随时间的演化。数据可用于评估调整后的模型在以下三个任务上的表现：- 重建：评估预测训练所用相同时间步长时的性能；- 外推：评估预测训练所用时间范围之外更长时间的性能；- 补充：评估预测训练区间内不同采样时间步长时的性能。