A mass on a spring vibrates in simple harmonic motion at a frequency of 3.26 Hz and an amplitude of 5.76 cm. If the mass of the object of 0.218 kg, what is the spring constant

91.48N/m

Explanation:

In a spring-mass system undergoing a simple harmonic motion, the inverse of the frequency f, of oscillation is proportional to the square root of the mass m, and inversely proportional to the square root of the spring constant, k. This can be expressed mathematically as follows;

=            -----------(i)

From the question;

f = 3.26 Hz

m = 0.218kg

Substitute these values into equation (i) as follows;

=                            [Square both sides]

()² = ()²()    

() = ²()                      [Take to be 3.142]

() = ²()

() = ()

() = ()                            [Switch sides]

() = ()                            [Re-arrange]

() = ()                            [Cross-multiply]

k = 8.608 x 10.6276

k = 91.48N/m

Therefore, the spring constant of the spring is 91.48N/m

i'm thinking more like energy

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

hope this !