Physics questions

[TrueTears]

also what's the difference b/w angular frequency and just frequency for a mass stuck on the end of an oscillating spring undergoing harmonic motion?

Also how do you do the question attached? I know a) has something to do with 0.5m(v_max)^2 = 0.5mv_x^2 + 0.5kx^2

thx man

[/0]

The difference is really just the definitions.
a)


So

Then since

from conservation of energy

b) , so



So quadruple k to double f.

[TrueTears]

farkk man, ur such a sikkent!!! thanks

also for b) how did u know it asked for angular freq, how come its not just normal freq? lolz i know the different formulas for each but what do they represent physically can u explain?

thanks

[/0]

I don't know any other reason than convenience

is the oscillator equation, which has solution

So if you let it's just.. convenient

In quantum mechanics we almost always use simply because it's too much of a bother to write out all the time.

Physicists like making lots of substitutions and simplifications, which can be really annoying sometimes.

My lecturer said that one time a string theorist who came to lecture said, "for simplicity, let , , , " etc.
Still not as lazy as mathematicians though.

[TrueTears]

bahahaha, thanks!!! i get it now

lol so many formulas to memorise, coz theres so many diff forms


doing damped oscillations atm, i bet ill have more questions coming up lol

[/0]

yeah lol :/
I never really memorised many of them

As long as you remember that

where



Then you should be ok. The rest can be derived with algebra and calculus.

[TrueTears]

lolz yeah that's how i do things with maths, i dislike memorising formulas, but i cant derive any physics formulas, so i leave it to my memorising brain  :knuppel2: :knuppel2:

[TrueTears]

anyways got a Q on damped oscillations

any help would be appreciated!!

[/0]

I never actually learned damped oscillations

Did you try this?

 



(wikipedia)

Assuming the natural period is the damped period, then

So

In 25 seconds, the amplitude reduces to 37% of the original

So



are you allowed to use a graphics calc?


As for the next part, max damping occurs when the speed is maximum, since the damping is attached to a term.... hmm

And max restoring is as usual at the maximum and minimum displacement.

[TrueTears]

Only scientific

but yeah ur working makes sense tho, but how the heck to solve for b LOL

[/0]

Actually nvm, it can't work... only allows , which can't solve the problem


Unless the problem actually means that , in which case solving for is easy.

[TrueTears]

A sinusoidal wave travelling in the positive x direction has the equation

I know k is the wave number, is the angular frequency but what is ? Book says its the phase constant, but how does one work it out? Eg consider the following Q attached. Can you show me how to do it?

[/0]

You simply plug in , and and solve for

[TrueTears]

oh so its like initial conditions?

[/0]

Yeah pretty much.