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Evgen [1.6K]
3 years ago
5

A 20-kilogram mass is attached to a spring. If the frequency of simple harmonic motion is 2/p cycles/s, what is the spring const

ant k? What is the frequency of simple harmonic motion if the original mass is replaced with an 80-kilogram mass?
Mathematics
1 answer:
SVEN [57.7K]3 years ago
3 0

Step-by-step explanation:

Frequency of a mass-spring system is:

f = √(k/m) / (2π)

Given f = 2/π Hz and m = 20 kg:

2/π Hz = √(k / 20 kg) / (2π)

4 Hz = √(k / 20 kg)

16 s⁻² = k / 20 kg

k = 320 kg/s²

k = 320 N/m

If the 20 kg mass is replaced with an 80 kg mass, the frequency is:

f = √(320 kg/s² / 80 kg) / (2π)

f = √(4 s⁻²) / (2π)

f = 2 Hz / (2π)

f = 1/π Hz

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