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2 identical springs were put Vertically. if one was pulled 5cm (spring1) and the other was pulled 10cm(spring2) and were left to move a simple harmonic motion would the periodic time for (spring2)be double the periodic time for (spring1).

The answer is wrong i think but i have to mathematically prove it so my teacher don't think i am doing it randomly

i think its wrong because according to the law for the periodic time

T=[tex]2\pi\ [/tex] x [tex]\frac{\sqrt{m}}{\sqrt{k}}[/tex]

and k =f/x and since x is in the root it even if we double it we won't get double T or something like that?