1. An impact system has a weight  and a spring constant , where  and  are independent. If the system is dropped from , determine the mean and standard deviation of the maximum spring force using the First Order Second Moment Method. Ignore the mass of the spring.

Solution

Let the maximum deflection of the spring be . According to conservation of energy

Then

Solving for  yields

By taking the positive root, the maximum deflection of the spring is

Then the maximum spring force is given by

Using FOSM, we have

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