Understanding Simple Harmonic Motion: Equations and Parameters Explained

[lovelylila]

I'm confused on part of an AP Physics lab on "Simple Harmonic Motion from a Force Perspective." Using a hanging spring & mass, motion detector, and CBL unit/Ti-83 graphing calculator, we used the calculator's graphs to create equations that included the amplitude, angular frequency, the phase offset -- y(t)= Acos(wt + symbol for phase offset). One follow-up question is how each parameter (amplitude, angular frequency, and phase offset) would change if you repeated the experiment using a larger amplitude.

Obviously, the amplitude would change. But what about angular frequency-- do amplitude and angular frequency have any sort of relationship? I've looked at all the equations I've been given in this chapter (such as w= square root (k/m) ) and all the equations relating angular frequency to period, but can't seem to find anything. Can anyone give me a nudge in the right direction here? I'd really appreciate it. :-)

Also, would changing the mass hanging off the end of the spring affect the amplitude? I realize it would change the angular frequency because of the above equation, but... Again, I feel really stupid but I can't seem to find the relationship-- any slight nudges would be very much appreciated! :-)

 

[rl.bhat]

Amplitude is decided by how much you pull the spring from its mean position. It does not depend on the mass hanging off the spring. And chnage in amplitude does not change the other parameter of SHM.

 

[ogb p]

I can understand your confusion and would be happy to provide some guidance on the concepts of simple harmonic motion and how they relate to the parameters mentioned in your lab.

Firstly, let's define what simple harmonic motion is. It is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. This means that as the object moves away from its equilibrium position, a force is applied to bring it back towards the equilibrium position. This results in a back-and-forth motion that repeats itself over time.

Now, let's look at the parameters you mentioned - amplitude, angular frequency, and phase offset. Amplitude is the maximum displacement of the object from its equilibrium position. It is directly related to the energy of the system and will change if the energy changes. So, if you repeat the experiment using a larger amplitude, the amplitude parameter in your equation will also change.

Angular frequency, on the other hand, is related to the mass and stiffness of the system. In your equation, w= square root (k/m), the angular frequency is inversely proportional to the square root of the mass. This means that as the mass increases, the angular frequency will decrease. So, if you change the mass hanging off the end of the spring, it will affect the angular frequency and therefore, the period of the motion.

Lastly, the phase offset is a measure of the initial displacement of the object from its equilibrium position at t=0. It does not have a direct relationship with the amplitude or angular frequency. However, it is important in understanding the initial conditions of the system and how it affects the motion.

In summary, changing the amplitude will affect the amplitude parameter in your equation, changing the mass will affect the angular frequency, and the phase offset is a measure of the initial displacement of the object. I hope this helps to clarify your understanding of simple harmonic motion and its parameters. Keep up the good work in your AP Physics lab!