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