Understanding Oscillation Frequencies and Mass Ratios in Elastic Systems

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Understanding oscillation frequencies in elastic systems involves recognizing how mass affects frequency. The relationship between frequency and mass is inversely proportional; as mass increases, frequency decreases. In the given example, when the mass is quadrupled, the frequency of oscillation is halved, resulting in a frequency change factor of 1/2. This concept can be confusing, but mastering the manipulation of equations is key to solving related problems. Clarifying these relationships can significantly improve performance on tests.
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Ok. here's the deal. since i have started physics, i have been having problems with this concept. when you have an equation that has two sides to it, such as sqroot(F/m/l)=freq(wavelength) and they adjuct one side, how do you know what to do the other side?

For example, the question is "An object is attached to a spring and its frequency of oscillation is measured. Then another object is connected to the first object, and the resulting mass is four times the original value. By what factor is the frequency of oscillation changed?"- the answer is 1/2 but how?!
I keep getting these problems wrong on tests and it seems like everyone gets it except me! PLEASEEEEEE help :(
 
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nevermind i think i get this noqw
 

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