Answer to Question #283277 in Physics for riki

Question #283277

Two springs are

joined and connected to a block of

mass 0.245 kg that is set oscillating

over a frictionless floor. The springs

each have spring constant k $

6430 N/m. What is the frequency of

the oscillations?


1
Expert's answer
2021-12-28T13:36:32-0500

Let's suppose that the two springs connected in series with each other. Then, we can find its total spring constant as follows:


1ktot=1k1+1k2,\dfrac{1}{k_{tot}}=\dfrac{1}{k_1}+\dfrac{1}{k_2},1ktot=1k+1k=2k,\dfrac{1}{k_{tot}}=\dfrac{1}{k}+\dfrac{1}{k}=\dfrac{2}{k},ktot=k2.k_{tot}=\dfrac{k}{2}.

Finally, we can find the frequency of oscillations as follows:


f=12πktotm=12πk2m,f=\dfrac{1}{2\pi}\sqrt{\dfrac{k_{tot}}{m}}=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{2m}},f=12π6430 Nm2×0.245 kg=18.2 Hz.f=\dfrac{1}{2\pi}\sqrt{\dfrac{6430\ \dfrac{N}{m}}{2\times0.245\ kg}}=18.2\ Hz.

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