A force sensor has a mass of 0.5 kg, stiffness of 2×102 Nm−1, and a damping constant of 6.0N s m−1. 

1. Calculate the steady-state sensitivity, natural frequency, and damping ratio for the sensor.

 2. Calculate the displacement of the sensor for a steady input force of 2 N. 

3. If the input force is suddenly increased from 2 to 3 N, 

derive an expression for the resulting displacement of the sensor.