Calculating Amplitude in Simple Harmonic Motion

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SUMMARY

The discussion centers on calculating the amplitude in Simple Harmonic Motion (SHM) using the formula A = √(c₁² + c₂²), where x(t) = c₁cos(wt) + c₂sin(wt). A participant expresses confusion regarding the derivation of the amplitude from the given parameters. The correct amplitude is determined by the equilibrium point of the block, calculated as 0.05g/k = 0.01 m, with the initial position at 0.03 m, indicating that the excess distance represents the amplitude. This clarification resolves the initial confusion about the calculation process.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Familiarity with trigonometric functions and their applications in physics
  • Knowledge of equilibrium points in oscillatory systems
  • Basic grasp of the relationship between force, mass, and acceleration (F = ma)
NEXT STEPS
  • Study the derivation of amplitude in Simple Harmonic Motion using different examples
  • Learn about the role of equilibrium points in oscillatory motion
  • Explore the effects of damping on amplitude in SHM
  • Investigate the mathematical modeling of SHM using differential equations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to Simple Harmonic Motion.

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My question is with part c, more specifically the calculating of the amplitude part.
[PLAIN]http://img691.imageshack.us/img691/1750/shmquestion.jpg

The answer to the question is:
[PLAIN]http://img80.imageshack.us/img80/8921/shmanswer.jpg

I do not understand how to arrive at this conclusion in order to calculate the amplitude; it baffles me. Any poking or prodding in the right direction (or even an outright answer) would be greatly appreciated.
 
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Isn't the amplitude

A = \sqrt{c^2_1 + c^2_2}

Where

x(t) = c_1cos(wt) + c_2sin(wt)
 
I have no idea unfortunately. My question is how did the examiner arrive at the answer above (it is the verbatim answer for the past paper I'm currently working on).
 
see the equilibrium point of smaller block is .05g/k = .01 m but initially it is at .03 m thus this excess distance is its amplitude . as after each oscillation it wll come back to this point .
 
Thank you very much, that actually kind of makes sense now!
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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