Answer to Question #283277 in Physics for riki

Question

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?

Answer 1

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

$$\dfrac{1}{k_{tot}}=\dfrac{1}{k_1}+\dfrac{1}{k_2},$$ $$\dfrac{1}{k_{tot}}=\dfrac{1}{k}+\dfrac{1}{k}=\dfrac{2}{k},$$ $$k_{tot}=\dfrac{k}{2}.$$

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

$$f=\dfrac{1}{2\pi}\sqrt{\dfrac{k_{tot}}{m}}=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{2m}},$$ $$f=\dfrac{1}{2\pi}\sqrt{\dfrac{6430\ \dfrac{N}{m}}{2\times0.245\ kg}}=18.2\ Hz.$$