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 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.

A) What is the period for the oscillation?

B) Estimate the effective mass participating in the oscillation. This is the mass of the bell itself plus the mass of the water.

C) 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?

1) .75s

2) 0.01709kg
3) not sure.

A) To determine the period of the oscillation, we need to find the time it takes for one complete cycle. In the given graph, the distance between two consecutive peaks of positive displacement represents one complete cycle. Let's call this distance "d". From the graph, we can measure the time it takes to travel this distance, which we will call "t". The period can then be calculated as the ratio of distance to time, so it is given by:

Period (T) = d / t

B) The effective mass participating in the oscillation is the sum of the mass of the jellyfish's bell and the mass of the water contained within it. Unfortunately, the mass values are not provided in the given information, so we cannot directly estimate the effective mass.

C) The graph shows a damped oscillation, meaning that the amplitude of the oscillation gradually decreases over time. We can analyze this by comparing the amplitude of the first peak of positive displacement with that of the next peak in the same direction.

The factor by which the amplitude decreases over one period is given by:

Amplitude decrease factor = Amplitude(first peak) / Amplitude(next peak)

Using the given graph, we can measure the amplitudes of the peaks and calculate this factor.

Once we have the amplitude decrease factor, we can calculate the time constant for damping. The time constant (τ) is defined as the time it takes for the amplitude to decrease by a factor of 1/e (where e is the base of natural logarithms, approximately 2.71828). We can derive the time constant by dividing the period (T) of the oscillation by the natural logarithm of the amplitude decrease factor:

Time constant (τ) = T / ln(Amplitude decrease factor)