SHM...

[sps27]

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Which of the following is NOT a simple harmonic motion?

a. An electron moving back and forth in ac current
b. The orbit of the earth around the sun as viewed from the side
c. A pendulum swinging at a small angle
d. A boy bouncing a yoyo in a steady rthythm

Answer is (d).

So a child on a swing, swinging back and forth, will that be considered an SHM? I guess what is the defining quality of SHM, which makes it different from a cyclical motion? Is restoring force a defining quality?

Also, not related to the above but just a couple of general questions, 1) is there any eqn which relates 'density with temp'? 2) does Intensity of sound vary squarely with Amplitude or linearly?

 

[DrknoSDN]

SHM is sinusoidal motion.. I would guess they are saying the yoyo springs back up at the bottom because of the boy..
Cause if you just let a friction-less yoyo fall and return, (if it returned to the starting height without the assistance of the boy), i would say that would be SHM also.
Also (c) a pendulum at a very extreme swing is not harmonic because if you look at a vertical position vs velocity it goes from being circular (small angle) to elliptical (large angle)

Sound intensity varies with the square of the Amplitude.
Not sure about density vs temp. I think that is due to a ton of organic chem molecular bonding factors. There are general rules but like water can hydrogen bond so it's density varies with temperature but it is at it's most dense around 4 degrees Celsius. Lower or higher and the density decreases. And with a gas if you increase temperatures the volume changes so it's density goes down (hot air balloon),, but if you have constant volume increasing the temp only changes the pressure.

TLDR, no density does not relate to temp in an equation.

 

[sps27]

SHM is sinusoidal motion.. I would guess they are saying the yoyo springs back up at the bottom because of the boy..
Cause if you just let a friction-less yoyo fall and return, (if it returned to the starting height without the assistance of the boy), i would say that would be SHM also.
Also (c) a pendulum at a very extreme swing is not harmonic because if you look at a vertical position vs velocity it goes from being circular (small angle) to elliptical (large angle)

Sound intensity varies with the square of the Amplitude.
Not sure about density vs temp. I think that is due to a ton of organic chem molecular bonding factors. There are general rules but like water can hydrogen bond so it's density varies with temperature but it is at it's most dense around 4 degrees Celsius. Lower or higher and the density decreases. And with a gas if you increase temperatures the volume changes so it's density goes down (hot air balloon),, but if you have constant volume increasing the temp only changes the pressure.

TLDR, no density does not relate to temp in an equation.

Thanks for the response. I appreciate it. I thought about it a little more about the boy bouncing the yoyo and I guess what I came up with is that in SHM, acceleration is not constant. It varies. Whereas a boy bouncing a yoyo, acceleration due to gravity is constant for the upward motion of yoyo, so perhaps that is why it is not SHM. I agree with the pendulum and the angle being small and large angle not being SHM. I've read that. Thanks for clearing up the amplitude bit. I appreciate it.