00:02
For resonance, her frequency must match the resonant frequency f -0, and this is equal to omega -not over 2 -pi, which is 1 over 2 -pi, and omega -not can be written as the square root of k over m.
00:28
And these values are all known, that's 1 over 2 pi times the square root.
00:35
The force constant k is given as 7 times 10 to the 2 newton per meter the mass of the baby is 12 .5 kg and so we get a resonant frequency of 1 .19 hertz now we wish to calculate the amplitude of the oscillation we know that x is equal to a cost omega t and from here we can see that v which is the derivative of x with respect to t is equal to minus a omega sine omega t and if we derive this once more we get the acceleration a acceleration a is dvd t which is minus a omega squared cos omega t and from here, the maximum acceleration, we can see a max is a omega squared.
02:15
Well, why is this important? when this becomes equal to the acceleration due to gravity, the normal force exerted on her by the mattress will drop to 0 at one point in the cycle.
02:26
And hence, a omega squared will be equal to g.
02:36
And from here, you can see that the amplitude a is equal to g over omega squared.
02:55
And that's g over k over m, which we know as an expression for omega squared...