Spring scales work by measuring the displacement of a spring that supports both the platfo...

Spring scales work by measuring the displacement of a spring that supports both the platform of mass mp and the object, of mass m, whose weight is being measured. Most scales read zero when no mass m has been placed on them; that is, they are calibrated so that the weight reading neglects the mass of the platform mp. Assume that the spring is linear elastic with spring constant k.

Figure P3.100

If the mass m is gently placed on the spring scale (i.e., it is dropped from zero height above the scale), determine the expression for maximum speed attained by the mass m as the spring compresses.