Physics
hawaiiangurl
2016-04-09 21:57:57
A 0.520 kg mass suspended from a spring oscillates with a period of 1.50 s. how much mass must be added to the object to change the period to 2.05 s?
ANSWERS
patnburt
2016-04-10 01:41:40

[latex]Given:\m_1=0.520kg\T_1=1.50s\T_2=2.05s\\Find:\Delta m=?\\Solution:\\Delta m=m_2-m_1\\T=2 pi sqrt{ frac{m}{k} } Rightarrow 2 pi = frac{T}{sqrt{ frac{m}{k} }} \\frac{T_1}{sqrt{ frac{m_1}{k} }} =frac{T_2}{sqrt{ frac{m_2}{k} }} \\T_1sqrt{ frac{m_2}{k} }} =T_2sqrt{ frac{m_1}{k} }} \\frac{T_1^2m_2}{k} =frac{T_2^2m_1}{k} \\T_1^2m_2=T_2^2m_1Rightarrow m_2= frac{T_2^2m_1}{T_1^2} \\Delta m=frac{T_2^2m_1}{T_1^2} -m_1=m_1(frac{T_2^2}{T_1^2} -1)[/latex] [latex]\\Delta m=0.520kg( frac{(2.05s)^2}{(1.50s)^2} -1)approx 0.4512kg[/latex]

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