Mass added to a spring to increase period of oscillation

AI Thread Summary
To increase the period of oscillation of a mass on a spring by a factor of two, the total mass must be increased to three times the original mass. The relationship between the period (T) and mass (m) is given by T = 2π√(m/k), indicating that T is proportional to the square root of m. By setting the new period to 2T, the equation simplifies to show that the additional mass needed is 3m. This conclusion clarifies the confusion regarding the correct answer, which is 3m. Understanding the proportional relationship between mass and period is crucial for solving such problems.
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Homework Statement



7. Mass m is oscillating on the end of a spring. How much mass must be added in order for the
period of oscillation to increase by a factor of two?
A.m
B.2m
C.3m
D.4m
E.8m

Homework Equations



f=-kx
w= \sqrt{k/m}
T = 2\pi\sqrt{m/k}

The Attempt at a Solution



since period (T) is proportional to the square root of m and we want 2t, i had 2T=\sqrt{m} so 2^2 =4

the given answer is 3 and i don't know how this was chosen
 
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You found the factor by which the total mass has to increase. But what do they ask for?
 
yeah that makes sense haha 4xm =4m - m that i started with is 3m
thanks a lot it was blowing my mind
 

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