A laptop computer of mass "m" is wrapped in a rigid container for shipment as shown in Figure P8. The equivalent stiffness of the wrapping material is "K" and the equivalent viscousdamping is "E". Consider scenarios where the package is accidentally dropped on the floor. Neglect the mass of the wrapping material (foam or plastic bubble sheets). a) Write the equation of vertical motion for the laptop computer. b) Determine: -the vertical displacement response u(t) of the laptop when the container is in contact with the ground/floor with initial velocity V (at time t =0). - the force transmitted to the laptop p(t). - the vertical acceleration a(t) of the laptop. c) Plot the response indicators listed in b) assuming the laptop computer has a mass m =2 kg; the foam packaging has a compressive stiffness of 500 N/cm and provides an equivalent viscous damping ratio of about 6% critical, and V = 500 cm/s. d) From the plots in c) determine the maximum displacement response of the laptop in the box and the corresponding time (max); the maximum force transmitted to the laptop and the corresponding time (tmax); the maximum acceleration f the laptop and the corresponding time (max). e) Repeat c) and d) if the package is dropped from a height of 1 m with no initial velocity. f) Can you estimate the maximum force the laptop will sustain if it is dropped from the same height of 1 m without its packaging? State your reasonable assumptions to simplify the shock load felt by the laptop. Figure P8 Rigid container Foam/plastic bubble wrap packaging (white space all around) V LAPTOP COMPUTER mass m Floor