Problem 3) The shock from dropping a computer can easily damage hard drives. You are asked to design a shock-protection system to reduce the maximum forces due to shock. (Note that the additional cost of buying a computer with solid-state memory would be a few hundred dollars - so you need to come up with a cheap design) Hard Drive Computer Ground Let us attempt a simple spring as the shock protection system and use the structural damping factor of 0.01 (under-damped). The mass is 100grams. The main challenge is the sleek design of the laptop; this limits the maximum allowable displacement to be say 0.5cm (i.e., the height difference between the hard drive and the computer casing) a) Find an expression for the displacement of the hard drive when it is dropped from rest at a height H on to a hard surface (ground). (Assume that the computer sticks to the ground after contact.) Note that the system is under-damped. Clarify how the gravity force influences (or not influence) the response b) Find an expression for the force acting on the hard-drive once it hits the ground c) Find a linear spring (i.e., find spring constant K) that would minimize the largest force on the hard drive when it is dropped from 5cm height on to a hard surface without exceeding the maximum displacement limit of 0.5cm d) What is the effect of increasing the spring constant on the force and max displacement? e) Plot the displacement and force as a function of time for your desigin f) Optimize both the spring constant and the damping factor Problem 3) The shock from dropping a computer can easily damage hard drives. You are asked to design a shock-protection system to reduce the maximum forces due to shock. (Note that the additional cost of buying a computer with solid-state memory would be a few hundred dollars - so you need to come up with a cheap design) Hard Drive Computer Ground Let us attempt a simple spring as the shock protection system and use the structural damping factor of 0.01 (under-damped). The mass is 100grams. The main challenge is the sleek design of the laptop; this limits the maximum allowable displacement to be say 0.5cm (i.e., the height difference between the hard drive and the computer casing) a) Find an expression for the displacement of the hard drive when it is dropped from rest at a height H on to a hard surface (ground). (Assume that the computer sticks to the ground after contact.) Note that the system is under-damped. Clarify how the gravity force influences (or not influence) the response b) Find an expression for the force acting on the hard-drive once it hits the ground c) Find a linear spring (i.e., find spring constant K) that would minimize the largest force on the hard drive when it is dropped from 5cm height on to a hard surface without exceeding the maximum displacement limit of 0.5cm d) What is the effect of increasing the spring constant on the force and max displacement? e) Plot the displacement and force as a function of time for your desigin f) Optimize both the spring constant and the damping factor
