A paramedical staff nurse improvises a second's pendulum with time period $$2\ \text{s}$$ by fixing one end of a string of length $$L$$ to a ceiling and the other end to a heavy object of negligible size. Within $$60$$ oscillations of this pendulum, she finds that the pulse of a wounded soldier beats $$110$$ times. A symptom of bradycardia is pulse less than $$60$$ per minute and that of tachycardia is greater than $$100$$ per minute. Then the length of the string is nearly and soldier has symptoms of