What Is the Speed of an Oscillating Particle at Equilibrium?

[BvU]

PS personally I would never trade in the perfectly correct value of $6\pi$ m/s for an approximate answer (18.7 m/s w is a wrong rounding off for 18.8495559215... ) unless I was really forced to do so. After all, in subsequent calculations factors $\pi$ may well cancel out.

 

[goonking]

PS personally I would never trade in the perfectly correct value of $6\pi$ m/s for an approximate answer (18.7 m/s w is a wrong rounding off for 18.8495559215... ) unless I was really forced to do so. After all, in subsequent calculations factors $\pi$ may well cancel out.

very true, ill keep that in mind

 

[BvU]

Draw a straight line with slope 3 m/s through the point (1.5s, 0 m) to check...

Where did the 2.5 s come from ? Not from me.

 

[goonking]

Where did the 2.5 s come from ? Not from me.

oh, i thought i needed to check by plotting the line at 2.5 secs with slope 6 pi.

but yes, before the 2.5 was a mistake i made :(

 

[BvU]

I'm lagging with my slow typing.

Acquiring some "dexterity" with sines and cosines is a good idea.
This exercise helps, but the $A$ and $\omega$ obfuscate things a bit (intentionally, from the point of viewof the exercise composer). For you, practicing with $x = \sin (\omega t)$ is more helpful (i.e. A = 1 and $\omega = 1$).

Draw a graph of that and a unit circle on the same scale to the left and tadaa: values of x and speed at the angles $0, {\pi\over 6}, {\pi\over 4}, {\pi\over 3}, {\pi\over 2}, {2\pi\over 3}, {5\pi\over 6}, {\pi}$ and each of these + ${\pi}$ become clear.

See how they all hang together, and also hang together with ${d^2x\over dt^2} = -x$.

Once you have that internalized, dealing with $A\ne 0$ and $\omega \ne 0$ is a piece of cake and your efficiency in excercises will improve; also: you don't have to remember all that much.

 

[goonking]

I'm lagging with my slow typing.

Acquiring some "dexterity" with sines and cosines is a good idea.
This exercise helps, but the $A$ and $\omega$ obfuscate things a bit (intentionally, from the point of viewof the exercise composer). For you, practicing with $x = \sin (\omega t)$ is more helpful (i.e. A = 1 and $\omega = 1$).

Draw a graph of that and a unit circle on the same scale to the left and tadaa: values of x and speed at the angles $0, {\pi\over 6}, {\pi\over 4}, {\pi\over 3}, {\pi\over 2}, {2\pi\over 3}, {5\pi\over 6}, {\pi}$ and each of these + ${\pi}$ become clear.

See how they all hang together, and also hang together with ${d^2x\over dt^2} = -x$.

Once you have that internalized, dealing with $A\ne 0$ and $\omega \ne 0$ is a piece of cake and your efficiency in excercises will improve; also: you don't have to remember all that much.

thanks for the advice :)

 

[BvU]

Welcome. Good luck with your physics binge.

More advice: get some rest when wearing out !

 

[goonking]

Welcome. Good luck with your physics binge.

More advice: get some rest when wearing out !

hehe, no rest for me.