As the captain of the scientific team sent to Planet Physics, one of your tasks is to measure g. You have a long, thin wire labeled 1.73 g/m and a 1.30 kg weight. You have your accurate space cadet chronometer but, unfortunately, you seem to have forgotten a meter stick. Undeterred, you first find the midpoint of the wire by folding it in half. You then attach one end of the wire to the wall of your laboratory, stretch it horizontally to pass over a pulley at the midpoint of the wire, then tie the 1.30 kg weight to the end hanging over the pulley. By vibrating the wire, and measuring time with your chronometer, you find that the wire's second harmonic frequency is 200 Hz . Next, with the 1.30 kg weight still tied to one end of the wire, you attach the other end to the ceiling to make a pendulum. You find that the pendulum requires 313 s to complete 200 oscillations. Pulling out your trusty calculator, you get to work.
What value of g will you report back to headquarters?

The value of g is  

Explanation:

From the question we are told that

     The mass of the weight is

      The spring  constant  

       The second harmonic frequency is

       The number of oscillation is

        The time taken is  

Generally the frequency is  mathematically represented as

At second harmonic frequency the length of the string vibrating is equal to  the wavelength of the wave generated

Noe from the question the vibrating string is just half of the length of the main string so

Let assume the length of the main string is  

So      

The velocity of the vibrating string is mathematically represented as

Where T is the tension on the string which can be mathematically represented as

So  

Then

=>      

=>      

=>        

substituting values

Generally the period of oscillation is mathematically represented as

=>  

   The period can be mathematically evaluated as

 substituting values

Therefore

so

substituting for L

=>    

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