Homework Help: Physics

Posted by Justin on Thursday, February 18, 2010 at 7:00pm.

A fisherman's scale stretches 4.2 cm when a 3.0 kg fish hangs from it.
What will be the amplitude and frequency of vibration if the fish is pulled down 2.3 cm more and released so that it vibrates up and down?

Physics - Damon, Thursday, February 18, 2010 at 7:16pm
F = -k x
k = 3 *9.8 / .042 Newtons/meter

assume x = .023 sin 2 pi f t
then acceleration = - .023 (2 pi f)^2 sin 2 pi f t

so
-k x = -.023 (2 pi f)^2 sin 2 pi f t

- 3 * 9.8/.042 * .023 sin 2 pi f t =
- 3* .023 (2 pi f)^2 * sin 2 pi f t
so
(2 pi f)^2 = 9.8/.042

or you could use the formula
f = (1/2 pi)sqrt (k/m)

Note that m canceled out for me because it was in the spring constant k

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