How Does Changing Mass, Spring Stiffness, and Initial Energy Affect SHM?

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In summary, the conversation discusses a block on a spring in SHM and how the system would change if the mass is increased by 4 and if a stiffer spring is used. It also mentions how the amplitude and period are affected by changes in energy and how to find the traveling speed of a standing wave.
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Punkyc7
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My question is can someone just check my reasoning to make sure I am understand what is happening.

There is a block on a spring in SHM and it has an initial energy E that is given by stretching string. What would happen to the system if you increase the mass by 4 and you repeat the experiment exactly as before?

The period would increase by 2 and the amplitude would decrease by a half because E=½ kA^2=1/2mv^2





Now the experiment is repeated again with a stiffer spring. What changed in the system

The period would decrease and the amplitude would also decrease because the energy is held constant.






Now the experiment is repeated again with less energy from the initial stretch. What changes in the system.

Only the amplitude would decrease because the period is independent of amplitude.








another quick question how do you find the traveling speed of a standing wave y(x,t)=2Asin(kx)sin([itex]\omega[/itex]t)

I know the vertical speed is the partial with respect to t so would the horizontal be the partial with respect to x?
 
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The vertical speed is the partial derivative with respect to time and the horizontal speed is the partial derivative with respect to position. So in this case, the horizontal speed would be kA*cos(kx)*sin(\omegat).
 

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