Solve SHM: Max Acceleration | Physics Homework

AI Thread Summary
In the discussion about simple harmonic motion (SHM), the key focus is on the relationship between acceleration, velocity, and energy. The correct answer to the question posed is that maximum acceleration occurs when displacement is maximum, contradicting the initial assumption that it coincides with maximum velocity. The participant initially misinterpreted the acceleration equation due to a missing negative sign, which clarified the relationship between the variables. Additionally, it was noted that while maximum potential energy equals maximum kinetic energy under standard conditions, redefining the zero level of potential energy could allow for different interpretations of statements C and D. The conversation emphasizes the importance of understanding the fundamental principles of SHM to accurately analyze motion.
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Homework Statement


*Forgot to mention that this is a SHM question in the title
Which of the following statements about an object that which perform an Simple harmonic motion is true?
A) the acceleration is maximum when the velocity is maximum
B) the acceleration is maximum when the displacement is maximum
C) the maximum potential energy is greater than the maximum kinectic energy
D) the maximum kinectic energy is greater than the maximum potential energy

Homework Equations


x= A sin wt
v= Aw cos wt
a= Aw^2 sin wt

The Attempt at a Solution


At first i was choosing a because i believe c and d is not possible due to conversation of energy. But then i feeling like something wasn't right, so i went to check my references book on the graphs of x,v,a against t.
Which i found out that when a is maximum, v is 0 and when a is 0, v is maximum. So i change my answer to b. But the answer given is a. So i wonder why is it a
SHM1.gif

[/B]
 
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B is correct. Just note that you missed a minus sign in your acceleration expression. The graph is qualitatively correct. A is false.
 
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Orodruin said:
B is correct. Just note that you missed a minus sign in your acceleration expression. The graph is qualitatively correct. A is false.
Oh yeah i forgot to put the minus sign. Thanks for the quick answer
 
Also note that while answers C and D are both false with the standard choice of potential energy being zero at zero displacement from the equilibrium (the correct thing being that the maximum potential is equal to the maximum kinetic energy with that choice of potential), there is nothing stopping you from arbitrarily redefining the zero level of the potential energy. If you do, either C or D could be made to be correct.
 

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