Show that the effective mass of the oscillating system is approximately meff = 2

Question

Show that the effective mass of the oscillating system is approximately meff = 256 g. Hint: Use the temporal angular frequency 5.77 rad/s. How does your effective system mass compare to the mass of the hanging object, m = 200 g?

Y=0.11 m

Edit: I'm not sure what other information is missing. The equation used for the coordinate system is y(t) = Y cos( t +0 ) = (0.105m)cos 5.77 rad/s t + (1.30 rad). I know that temporal angular frequency=sqrt(k/msys), but I'm not sure where k comes from or if that's even what is being asked here.

Explanation / Answer

The spring constant is missing.

Had the spring been massless then the effective mass of the system would have been the same as the mass of the particle. But for spring with mass M, then the temporal angular frequency can be written as sqrt(k/(effective mass)) = sqrt(k/(M+m/3)).

So you see, in order to calculate the effective mass, you need to know the temporal frequency(given) and the spring constant(missing).

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