Question

A jellyfish can propel itself with jets of water pushed out of its bell, a flexible structure on top of its body. The elastic bell and the water it contains function as a mass-spring system, greatly increasing efficiency. Normally, the jellyfish emits one jet right after the other, but we can get some insight into the jet system by looking at a single jet thrust. (Figure 1) shows a graph of the motion of one point in the wall of the bell for such a single jet; this is the pattern of a damped oscillation. The spring constant for the bell can be estimated to be 1.2 N/m

Deflection (cm) 0.6 0.3 t (s) -0.3 -0.6

What is the period for the oscillation? 0.75s

Estimate the effective mass participating in the oscillation. This is the mass of the bell itself plus the mass of the water. 17.1 g

Consider the peaks of positive displacement in the graph. By what factor does the amplitude decrease over one period? Given this, what is the time constant for the damping?

Answer 1

a) T = 0.75 s

b) The frequency is given by:

$\omega = 2\pi/T$

then:

$m =k/ \omega^2 = 1.2/(2\pi/T)^2 = 0.0171 kg$

c) In one period:

$\frac{A_f}{A_o} = \frac{0.15}{0.6}=0.25$