Answer:
2.8 seconds
Explanation:
First let us write out the formula relating the period(T),mass(m) and spring constant(k)
[tex]T=2\pi \sqrt{\frac{m}{k}}\\[/tex]
let assume [tex]2\pi \frac{1}{\sqrt{k}}=constant=k[/tex]
hence w can write the formula as
[tex]T=k\sqrt{m}\\[/tex]
if we vary k, we arrive at
[tex]\frac{T_{1} }{\sqrt{m_{1}}}=\frac{T_{2} }{\sqrt{m_{2}}}=...=\frac{T_{n} }{\sqrt{m_{n}}}\\[/tex]
Now if the mass was doubled,
[tex]m_{2} =2m_{1} \\[/tex]
we arrive at
[tex]\frac{T_{1} }{\sqrt{m_{1}}}=\frac{T_{2} }{\sqrt{2m_{1}}}\\\frac{T_{1} }{\sqrt{m_{1}}}*{\sqrt{2m_{1}}}=T_{2} \\T_{1} *\sqrt{2}=T_{2}\\[/tex]
Since [tex]T_{1} =2seconds \\[/tex]
[tex]T_{2}=2*1.414\\T_{2}=2.8 seconds[/tex]
