Harmonic Motion 2: Sally & Mommy Ride the Least Exciting Carnival Ride

phySicNewB
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The world's least exciting carnival ride consists of a cloth sling (of negligible mass) hanging by a spring of force constant k = 225 N/m. Children sit in the sling and bob up and down slowly. How exciting ...

Little Sally tries the ride. She gets into the sling, and, after Cletus the Carny gives her a bit of a push, oscillates up and down with a period of 1.78 seconds.

"Mommy, mommy, help, it's scary!" cries Sally. Her mother replies, "Don't worry, dear, you can sit on my lap and we'll ride together."

Together, Sally and her mother bob up and down with a period of 3.32 seconds.

Cletus scratches his head for a moment, then derives the mass of Sally's mother. What is it?
 
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What have you attempted so far? You must have some idea of how to approach the problem. If not, tell us what you don't understand.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.

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