Frequency of oscillation (in Hz) question help Thanks

[nukeman]

Homework Statement

A 320 kg wooden raft floats on a lake in equilibrium. When a 75 kg man steps carefully onto the raft, it floats 3.5 cm deeper into the water. When he steps off, the raft oscillates for a while.

I figured out that the force constant is 21,000 Nm - first off, is that correct?

Now my QUESTION is, calculate the Frequency of oscillation (in Hz) after the man steps off the raft?

Homework Equations

The Attempt at a Solution

I came up with...

2pi sqrt (m/k)

2pi sqrt (320/21,000) = .776 Hrtz

 

[Delphi51]

I see you used the spring equation F = kx and found the k (agree with 21000).
I have some reservations about treating this situation like a spring, but it makes considerable sense and I can't think of an alternative. Anyway, continuing with the spring model, you would use
T = 2pi sqrt (m/k)
to find the period and then the frequency.

 

[Simon Bridge]

Your reasoning is more important than your results.

Treated like a mass on a spring?
(75x9.8)N was enough for 3.5cm extension is 21000Nm - well done.
You plugged that into the equation for period of a mass on a spring :(

$$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}=\frac{1}{T}$$