Question

2.1: Describe in your notebook how the following systems can be modeled like a spring undergoing simple harmonic oscillation:

• A diving board • A planet orbiting a star • A guitar string • The human circulatory system

2.2: Describe what might happen in one or two of the systems above if they were operating out of resonance. Turns out it’s a pretty important phenomenon!

Answer 1

Hey there!

First you should be having an idea of what a Simple Harmonic Motion (SHM) is.

As the word Harmony means, it happens with a rhythm or a tempo you could say. A SHM happens with a restoring force happening which is directly proportional to the displacement of the system , so that it restores back and continues the cycle again. I think you get the idea now.

When a diver stands on a diving board,and jumps the diving board bends down and repels back above its rest position and goes down again. Thus the diver gets that extra jump and he dives into the pool. You could notice that the diving board again goes in an up and down motion for a few seconds even after the diver has jumped. This rhythmic movement of the board can be related to the SHM.

When it comes to a planet which is orbiting a star, a planet revolves around when there is a balance between the forces of the space whivch is pulling the planet outward and the gravitational force by the star which is pulling the planet inward. This causes the planet to move around the star over and over again at an equal interval of time, thus resulting in a SHM.

When it is a guitar string, when the string is pluck, we could see that the string goes up and down at a particular frequency creating the sound. The frequency that the string produces gives a wave pattern in sound. The movement of the guitar string is itself a SHM. The sound waves produced by the string is also a SHM.

Well, in a Human circulatory system .... you should have guessed it by now. It is the rhythm of the heart beat that we could classify under the SHM. It simply happens with no distortion unless the system is disturbed .

Okay now let's see what would have happened if SHM wouldn't have existed in 2 cases here. The diving board and the circulatory system.

If there was no SHM or rhythmic motion of the flexing of the diving board. The diver wouldn't be able to get that extra jump by the flexing of the board. Or even if the board had flexing and no rhythm, the diver wouldnt be able to calculate the rhythm of his consecutive jumps that he does on the boards to increase his diving height before he dives. Thus the time interval of the SHM is also an important factor.

Now lets see in the case of oir circulatory system. You know that hospitals check our ECG. Imagine if there was no rhythm in our blood pumping. Imagine the graph accured in the ECG then. It would be mountains and plains on the graph with no clue of whats happening. The amplitude of the wave is also important to measure the pressure at which the heart pumps.

I hope you got the idea by now. Cheers :)