Natural frequency calculated theorectically and experimentally

AI Thread Summary
The discussion centers on calculating the natural frequency of a spring-mass system through theoretical and experimental methods, revealing discrepancies between the two results. Participants explore whether damping contributes to this difference, noting that while damping affects amplitude, it typically does not alter the natural frequency. Accurate measurements of the spring constant and mass are emphasized as critical for theoretical calculations. Questions arise regarding the consistency of the spring constant across deflections and the importance of measuring the spring's relaxed length. The conversation concludes that while damping may influence results, the damped frequency should not differ significantly from the natural frequency.
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Homework Statement



I was given a spring mass system and asked to calculate the natural frequency by theorectical analysis and by using experimental data.

There was a difference between the natural frequency calculated theorectically and experimentally.

I was asked to discuss the difference in results and I wanted to know if damping is the cause for the difference in results .
 
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What was the difference between theoretical and experimental results for natural frequency. Certainly damping would have an effect.

Are the spring constant and mass accurately measured?
 
for the theorectical analysis I was given the length of spring, the mass attached and the length of stretched spring.I used that to calculate spring constant and then calculate frequency.

for the experimental I was given the time for 20 oscllations for five different readings.

Found average time ,diivided by 20 to find period and found inverse of period to find frequency.

I think damping has an effecy but I have read online that damping only affects amplitude of oscillation not the period.
 
The natural frequency is not affected by damping, but the damped frequency can be different. However, the different may not be too different.

http://hypertextbook.com/chaos/41.shtml
http://en.wikipedia.org/wiki/Damping
http://hyperphysics.phy-astr.gsu.edu/hbase/oscda2.html#c2

Is the spring constant actually constant over the range of deflection?

Did one measure the relaxed length (unloaded) of the spring before and after the experiment?

Did one use the spring constant determined from the experiment in the theoretical calculations?
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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