1.

when a spring is cut into half its time period should remain same because mass halves and k doubles right ?

Answer»

, , where Time-period, MASS attached to the SPRING, spring-constant.Now if spring is CUT into half its spring-constant, k, doubles.Hence time period, T, is decresed by  times.The above explanation is valid only if spring is ideal, i.e. massless.A more general formula is ,here,  mass of spring.I believe you can find the MODIFIED time-period.



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