A baby bounces up and down in her crib. Her mass is 13.5 kg, and the crib mattress can be modeled as a light spring with force constant 682 N/m.

If she were to use the mattress as a trampoline—losing contact with it for part of each cycle—what minimum amplitude of oscillation does she require?

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  1. w = 2 pi f = sqrt(k/m)

    x = A sin wt

    v = A w cos wt

    a = -A w^2 sin wt

    max a = A w^2 = g
    g = A w^2
    A = g m/k

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  2. to damon. that doesnt help. be more detailed.

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  3. Damon is Stating that-

    F=1/T T=2*pi/w so T= 2pi/sqrt(k/m)
    using our values T=2pi/sqrt(682/13.50)=.884004
    Therefore F=1/.884004 -->=1.13121
    For the second part acceleration=Aw^2 which must equal the acc. of gravity(g)
    g=Aw^2 w=sqrt(k/m) so w=7.107638
    plugging into our equation the equation g=Aw^2: 9.8=A*(7.107638^2)
    9.8/50.518518=A, so A=.193988 meters
    which is about 19.39 cm

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