Simple Harmonic Motion

We have
E =

P2

2m

+

1

2

kx2
However, E =

1

2

ka(t)2, where A(t) is amplitude. Therefore,

1

2

kA(t)2 =

P2

2m

+

1

2

kx2 or p2+mkx2 = mkA(t)2
The equation of motion is a circle in phase space whose radius is decreasing due to the friction of the liquid.