Hi all,
I have done MD simulation for simple harmonic oscillator with initial conditions xo=1 and vo=1 but I have checked the phase space plots by varying k and m values.
Below I have attached the picture that contains phase space plots.
Can anyone please explain me why phase space plot is changing when changing k and m values??
Looking forward for your answers.
Thanks in advance.
ANJIBABU
I have had some preliminary thoughts on this, and considering the equation describing a Simple Harmonic Oscillator:
x(t) = A Cos(ωt + φ)
Where φ is the starting phase of the cosinusoid, and ω = sqr(k/m) = 2π / T
k and m depending on their size determine the period and frequency, and the amplitude and phase are determined by the starting position or φ and the velocity affected by k and m.
Whilst the velocity and acceleration oscillate with the same frequency as the position but with shifted phases. These phase or phases are not the same parameters as φ, instead these are the phases between the velocity and the acceleration vectors of the Cosinusoid waveform.
Changing k and m will affect the frequency of oscillation and in turn this will affect the velocity and acceleration of the cosinusoid, and also the shift in the phases between the velocity and the acceleration.
This shifting of the phases may explain the variations in the Phase Space plots.
Because your phase curve will follow the ellipse, mv2 + k x2 = m + k, as a consequence of energy conservation (kinetic + potential energy must be constant).
Frankly, you should be embarrassed having asked such a trivial question!
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Mechanics
- Classical Mechanics