If you experienced these lab questions or have knowledge about them, please help

Question

If you experienced these lab questions or have knowledge about them, please help me out answer them.

1) Your timing error can be as much as 0.2s. Why was it better to time twenty cycles and find the average time rather than to find the time for one cylce twenty times and average the results?

2) If you displace the end of the spring a little or a lot, in other words if you change the amplitude of the oscillation, the period will be exactly the same. How can this happen? what is the diffrent about the motion of the spring? How does this relate to the equations you used in this experiment?

Explanation / Answer

1. If you obeserve 20 cycles and note the time ( let it be T), the measured time could be    T ± error

    or    T ± 0.2 s, hence the error in time period will be      (T ± 0.2 - T) / 20   =  ± 0.01 s

   But if 20 individual measurements are made, each will have error of ± 0.2 s hence propogated error is

   20 * (t ± 0.2) / 20   =  ± 0.2 s.

   Clearly, first method will have more accurate results.

2.    Time period of oscillation     T =   2 * (m / k)

                 Since T is independent of amplitude A, time period will not change on changing amplitude. This is because the restoring force is variable (proportion to strech in spring F = - k * x) if it were constant, the period would not remain the same.

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