A seismometer is an instrument that measures the displacement of the ground where it is set up. A point on the ground can move in three degrees-of-freedom (in the plane tangential to the earth and normal to the earth). A model for a single degree-of-freedom seismometer that senses vertical displacement is shown below: The frame position, denoted u, is the system input -the frame is fixed to a concrete block embedded in the earth. During an earthquake, for example, the ground moves the concrete block and hence the frame. The seismometer output is the mass position, denoted y, measured relative to the moving frame. Thus, the position of the mass relative to an inertial frame is y u. The physical parameters are: m = 1kg, b = 0.1N/(m/s), and k = 0.0425N/m. Answer the following: 1. Derive the differential equation governing the mass position relative to the moving base. In other words, the dependent variable is y and the input is the ground position, u