\\\\(T = 2\\pi \\sqrt {\\dfrac{m}{k}}\\\\)When the spring is cut into four equal parts, the spring constant of one part will becomes 4k, therefore the new time period will become\\\\(T' = 2\\pi \\sqrt {\\dfrac{m}{k'}}\\\\)\\\\(T = 2\\pi \\sqrt {\\dfrac{m}{4k}}\\\\) \\\\(T'=\\dfrac{T}{2}\\\\)