6th April 2008 - 11:46 AM
It's undergoing harmonic motion with frequency 28Hz with amplitude 13mm = 1.3cm = 0.013m and assuming it starts at zero displacement (ie x=0 at t=0). Therefore it's position (ignoring the slight side to side motion from the see-saw) will be expressed as, taking x' = dx/dt etc,
x = 0.013sin(28*2pi*t)
To find this I've done the double integration of the harmonic equation x'' + wx = 0 for w = (2*pi*f)^2 with standard boundary conditions (I can walk you through this if needs be).
Force due to oscillation = F = ma = mx'' = m(-wx) = -m[(2*pi*28)^2]*0.013sin(28*2pi*t). This is extremised when |sin|=1.
So it'll be max/min when F = -/+0.013m[(2*pi*28)^2]. When F = -0.013m[(2*pi*28)^2] then it's being accelerated upwards, When F=-0.013m[(2*pi*28)^2] then it's being pulled downwards.
Now we add in gravity so the total force an object of mass m will feel is mg-m[(2*pi*28)^2]*0.013sin(28*2pi*t). The sign on the mg is because when the force is zero, you feel 1g (even though it's pulling you down). To get the G force found you divide this by mg (ie you divide by the weight of the object since 5g = 5 times usual weight etc) to get 1-(1/g)[(2*pi*28)^2]*0.013sin(28*2pi*t)
Thus the max G's will be 1+(0.013/g)[(2*pi*28)^2], experienced when the object begins to be pulled upwards and the min will be 1-(0.013/g)[(2*pi*28)^2]. This makes sense, because you feel heaviest in an elevator/lift when it accelerates upwards and lightest when it accelerates downwards.
All you need to do now is put in g=9.8 and use a calculator.