When the spring is replaced with a spring with double of initial spring constant k2 = 2k₁, the new period, T2, is [tex]\sqrt{\frac{1}{2} } \ T_1[/tex].
Period of the mass oscillation
The period of the oscillation of the mass or cart on the spring is given by the following formula;
[tex]T = 2\pi \sqrt{\frac{m}{k} } \\\\[/tex]
at a costant mass;
[tex]T_1\sqrt{k_1} = T_2\sqrt{k_2} \\\\T_2 = \frac{T_1\sqrt{k_1} }{\sqrt{k_2} }[/tex]
when spring constant is doubled, k2 = 2k1. the new period, T2 is determined as follows;
[tex]T_2 = \frac{T_1\sqrt{k_1} }{\sqrt{2k_1} } \\\\T_2 = \frac{T_1\sqrt{k_1} }{\sqrt{2} \times \sqrt{k_1} } \\\\T_2 = \frac{T_1}{\sqrt{2} }\\\\T_2 = \sqrt{\frac{1}{2} } \ T_1[/tex]
Thus, when the spring is replaced with a spring with double of initial spring constant k2 = 2k₁, the new period, T2, is [tex]\sqrt{\frac{1}{2} } \ T_1[/tex].
Learn more about period of oscillation here: https://brainly.com/question/20070798
#SPJ1
