Energy can be harvested from vibrations by using a damped harmonic oscillator with base excitation, providing a sustainable way of yielding energy. By solving the equations of motion for this oscillator and studying the steady state solution, an expression for the time-averaged power is obtained. Different damping values of the oscillator influence how much power is yielded. In this thesis, it is analytically shown that a constant damping value equal to $c_{v} = \frac{\sqrt{c_{m}^{2}\psi^{2}f_{s}^{2}+(f_{s}^{2}-1)^{2}}}{\psi f_{s}}$ yields the most time-averaged power for the case where there is no switch in damping value and when there is a singular arbitrary switch in damping value. It is numerically shown that this damping value also yields the most time-averaged power for multiple switches in the damping value.

The Ekman spiral is described by a coupled system of differential equations originally discussed by Walfrid Ekman (Ekman, 1905). This system is a simplified version of the Navier­Stokes equations. The differential equations, as discussed in Ekman’s paper, concern the currents of the ocean. However, it is also possible to interpret these equations so as to describe and predict the flow of wind. The research as presented is not only inspired by Walfrid Ekman’s original paper, but also by the master thesis from de Jong (2021). The main contribution of this thesis is to include the influence of a constant vertical wind speed on the classical Ekman spiral. After stuyding the classical Ekman spiral, the inclusion of a constant vertical wind speed is done step­wise. First, the vertical wind speed is discussed without having any vertical Coriolis forces. The classical Ekman spiral and the Ekman spiral with vertical wind, but no vertical Coriolis force, were solved exactly. Then, the vertical wind speed is included fully, giving rise to a non­linear coupled system of differential equations. For the non­linear system, an algorithm for solving it analytically using a general perturbation method is proposed. Next, the hodograph of the non­linear equations of motion including a constant vertical wind speed, is made using Euler’s Explicit numerical method and a shooting problem is solved.