A fisherman's scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant (b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5cm more and released so that it vibrates up and down ...

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Mathematics

Lainey Phillips

19 November, 00:06

A fisherman's scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant (b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5cm more and released so that it vibrates up and down ...

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Douglas Peck · Answer 1

Hooke's law states that F = - kx, so

k = - F/x = - ma / x = - 2.6kg · (-9.8m/s²) / (0.041m) = 621 N/m ← (a)

(b) f = (1/2π) · sqrt (k/m) = (1/2π) · sqrt (621N/m / 2.6kg) = 2.46/s = 2.46Hz

Amplitude is simply 2.1cm