In oscillatory flow, drag and inertial forces experienced by flat plates and cylinders depend on the Keulegan–Carpenter number. Here we demonstrate that this extends to an asymmetric hexagonal conic heave plate suitable for a point absorber wave energy converter. The forces on three geometric scales of this plate were measured throughout forced oscillation experiments in quiescent water. From these measurements, phase-invariant and phase-dependent coefficients of drag and added mass are calculated using the Morison equation. For low amplitude oscillations, the total force experienced by the plate is well-described by phase-invariant coefficients that scale with the Keulegan–Carpenter number. However, for larger oscillations, maximum forces are better described by phase-dependent coefficients. Flow visualization is used to interpret the phase variations.