Model an accelerometer of proof mass m, attached to a cantilever spring (k = Ewt/41 where E is Young's modulus, w is width, t is thickness, and 1 is length). Assume the mass of the spring does not contribute. Derive the scaling law for static displacement under an acceleration a. Then derive the scaling law for the natural frequency of the sensor. What are the advantages/disadvantages of scaling (in terms of what you find from the above analysis).