> For the complete documentation index, see [llms.txt](https://alpaca4d.gitbook.io/docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://alpaca4d.gitbook.io/docs/basics/time-history.md).

# Time History

A **time series** is the relationship between the time in the domain, $$t$$, and the load factor $$\lambda$$ applied to the loads of the pattern it is attached to:

$$
\lambda = F(t)
$$

Every [Load Pattern](/docs/basics/loads/load-pattern.md) needs one. In a static analysis the time is a pseudo-time and the series is usually `Constant` or `Linear`; in a transient analysis it is real time and the series carries the actual signal.

## Components in this tab

| Component                                                         | Nickname                    | $$\lambda(t)$$                              |
| ----------------------------------------------------------------- | --------------------------- | ------------------------------------------- |
| [Constant](/docs/basics/time-history/constant.md)                 | `Constant Time Series`      | A fixed factor, independent of time.        |
| [Linear](/docs/basics/time-history/linear.md)                     | `Linear Time Series`        | Proportional to time — a ramp.              |
| [Trigonometric](/docs/basics/time-history/trigonometric.md)       | `Trigonometric Time Series` | A sine wave over a time window.             |
| [Path](/docs/basics/time-history/path.md)                         | `Path Time Series`          | Arbitrary, from lists of times and values.  |
| [Read Time Series](/docs/basics/time-history/read-time-series.md) | `Read Time Series`          | A **Path** series read from a file on disk. |

## Choosing one

| The load                                                           | Use                  |
| ------------------------------------------------------------------ | -------------------- |
| Is on for the whole analysis — dead load, permanent equipment      | **Constant**         |
| Should ramp up to avoid a sudden jump in a non-linear run          | **Linear**           |
| Is harmonic — machine vibration, an idealised base motion          | **Trigonometric**    |
| Follows a recorded or arbitrary signal you already have as numbers | **Path**             |
| Follows a recorded signal that lives in a file                     | **Read Time Series** |

Every component also outputs a **Graph** — plug it into a Grasshopper *Quick Graph* or a chart to see the signal before running anything.