A fisherman's scale stretches 4.0 cm when a 2.8 kg fish hangs from it.?

Question

A fisherman's scale stretches 4.0 cm when a 2.8 kg fish hangs from it.

(a) What is the spring stiffness constant?

N/m

(b) What will be the amplitude and frequency of vibration if the fish is pulled down 2.1 cm more and released so that it vibrates up and down?

amplitude ___cm

frequency ___Hz

Answer 1

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Answer 2

No other information is given, so assume that the system is lossless, we're at the surface of the earth where the gravitational acceleration is 9.8 m/s^2, and this is a perfect harmonic spring.

A harmonic spring follows the equation

F = kx^2

where F is the force on the spring, x is the displacement, and k is the spring constant.  From that, you should be able to plug in and get your answer for (a).

For the second part, if this is high school physics, and equation should have already been derived or supplied to you for this situation.  If this is college physics, then you need to write down an equation that balances all the forces on the mass (the fish).  Include the force of the spring above, gravity, and F = ma when the fish is bouncing.  But remember that a, acceleration, is just the second derivative of x with respect to time.  You will then have an ordinary differential equation, with initial condition of X equal to -2.1 cm or -6.1 cm or some other number, depending on what coordinate system you pick.  It doesn't matter, the solution will end up being x = Asin(t+phi) + something, and A will be the amplitude of the bouncing.