Time period of a spring mass system is T. If this spring is cut into two parts whose lengths are in the ratio $$1$$:$$3$$ and the same mass is attached to the longer part. The new time period will be

Question

Infinity Learn · Accepted Answer

The spring mass system oscillates in SHM, time period of mass attached to a spring is $$T=2$$$$π$$$$mK---(1)$$ where $$m=mass$$ of oscillator, $$k=force$$ constant for length l of spring , restoring force F $$=$$ $$-kl----(2)$$ after spring is cut into $$2$$ parts in $$1$$:$$3$$ ration of length, for shorter part spring $$F=-k1l4$$ for longer part spring, $$F=-k23l4---(3)$$ divide equation (3) by (2)⇒$$k2=4k3---(4)$$ new time period of longer part spring is  $$T1=2$$$$π$$$$m4k3---(5)$$ divide equation (5) by (1) then $$T1=32T$$

Time period of a spring mass system is T. If this spring is cut into two parts whose lengths are in the ratio 1:3 and the same mass is attached to the longer part. The new time period will be

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