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
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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