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Differential Equation for a schematic harmonic oscillator. enter image description here

here are some pictures that i tried to solve but i don't know it is true or completely wrong.enter image description here

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Affan Ashraf
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    What have you tried? – Adrian Keister Jul 10 '19 at 18:55
  • Can anyone help me out of this? – Affan Ashraf Jul 10 '19 at 18:56
  • I tried it but actually I didn't find any solution – Affan Ashraf Jul 10 '19 at 18:58
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    Welcome to Math SE! When posting questions like this it is customary to include information about what you have tried before expecting any helpful responses. – DMcMor Jul 10 '19 at 18:58
  • You should’ve edited your original question with this additional information instead of cloning it. – amd Jul 10 '19 at 19:27
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    Presumably this is an exercise from some course of study that you’re undertaking. I’ll bet that there was an example of this sort of problem earlier in the material somewhere. Even if you can’t solve the resulting equation, you should at least be able to formulate a differential equation for this system by analogy with that example. You write that you didn’t find any solutions: did you at least get that far? If so, where did you run into difficulty in solving the equation? Edit your question to show those efforts. – amd Jul 10 '19 at 19:32

1 Answers1

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Hint.

Calling $X = x - x_0$ with $x_0 = \frac{m g}{k}$ we have

$$ m\ddot X = F - c\dot X - k X $$

Cesareo
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