Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2022 / Paper 1 / 10 / c / i / Solution

Sampling at $0.2$ Hz means $\Delta t=5$ s. The target times are therefore $5$, $10$ and $15$ s, all within the supplied observation range. For bracketing observations, linear interpolation gives $d(t)=d_i+(d_{i+1}-d_i)(t-t_i)/(t_{i+1}-t_i)$. ThusThe estimated displacements are $7.00$, $12.99$ and $8.98\mu \mathrm{m}$. Interpolation assumes approximately linear behavior within each interval; it does not recover any unobserved high-frequency motion.