5) The figure shows the phase space plot for a simple harmonic oscillator
(dashed) and the same oscillator with a retarding force applied (solid). Point
P represents the initial conditions of the oscillator in both instances. In the
diagram, you may assume each division along the position axis corresponds
to 0.1 m; along the velocity axis, 0.10 m/s.
Figure 1:
a Use conservation of energy to determine $\omega_o$ for the oscillator.
b For critical damping, show that $\dot{x} = -\beta x$ at large time.
c Is the damped oscillator critically damped or overdamped? Explain.
d Explain how you can tell that the damped oscillator is not under-
damped.
e If you said in part c that the oscillator is (critically damped, over-
damped), then draw how the phase space plot would be different if
the oscillator (starting at point P) were instead (overdamped, criti-
cally damped). Explain your reasoning
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