When the person stands in the center of the floor system sho

When the person stands in the center of the floor system shown in the figure, he causes a static deflection of the floor under his feet. If he walks (or runs quickly!) in the same area, how many steps per second would cause the floor to vibrate with the greatest vertical amplitude? Assume: elastic response of the floor and neglect floor\'s relatively small mass, ( his walking or running will excite vibrations with different frequencies)

Solution

Here for the solution

Weight

mg = mass x acceleration

Acceleration = 2 s/t^2

Lets call displacement or deflection as delta

Now substituting we get time period

t = 2 sqrt ( delta /g)

From which frequency is thus found as

F = 1/t

1/2 sqrt ( g/ delta ).

Thus solution can be found