Form and use periodic sine and cosine models

A record is made of the position of a vibrating sensor

Readings at equal time intervals are 0, 2, 4, 2, 0 mm. The observation window shows one rise and fall

The observations alone do not establish a periodic model. The extrema, period and phase anchor below are supplied for the separate calculation

Let y(t) be the position of a vibrating sensor, measured in mm, where t is measured in seconds

The maximum is \(4\) mm and the minimum is \(-4\) mm

The full period is \(10\) seconds

The modelling domain is \(\left[0,30\right]\) seconds