Question

Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

We have
$E =\frac{P^{2}}{2 m}+\frac{1}{2} k x^{2}$
However, $E=\frac{1}{2} k a(t)^{2}$, where $A(t)$ is amplitude.
Therefore, $\frac{1}{2} k A(t)^{2}=\frac{P^{2}}{2 m}+\frac{1}{2} k x^{2} $
or $ p^{2}+m k x^{2}=m k A(t)^{2}$
The equation of motion is a circle in phase space whose radius is decreasing due to the friction of the liquid.