- #1
richyw
- 180
- 0
Homework Statement
I have measured the amplitude between the first and tenth oscillations for a damped harmonic oscillator (spring with a mass attached). I also have measured the period. First question. Is an (underdamped) harmonic oscillator periodic? Like I know that the solution to the differential equation has a sine/cosine argument in it and it does oscillated with a period. But as time goes on the exponential decreases its amplitude. So can we really call this motion "periodic"?
Anyways my main question is how do I find the damping constant? In the equations section i'll put what my lab manual gives
Homework Equations
[tex]\frac{b}{2M}T=\ln\left(\frac{x_1}{x_2}\right)[/tex] where b is the damping constant, M is the mass, T is the period and [itex]x_1[/itex] and [itex]x_2[/itex] are the amplitude of the first and second oscillations respectively
The Attempt at a Solution
This makes sense to me, except for one thing. I do not understand what to do if I measured the 1st and 10th amplitude instead of the first and second. What is the proper way to handle this. The two things I can think of would be to divide the ratio I have by 9, and then just plug it in. I also thought I could use the ratio I have and then multiply the period of one oscillation (which I measured independently) by 9. Neither really makes sense to me though TBH.