# phy shm!!![10分]

shm 的 equilibrium position (e)係唔係第於個amplitude?

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shm 的 equilibrium position (e)係唔係第於個amplitude?

equilibrium position 是當這個系統還未有受到任何合外力作用時,即其Restoring Force = 0時的位罝,但是如果物體巳在VIBRATING,通常當物體通這一點時,其位移(displacement)會是0,但是其dx/dt (v)會是最大的.因為所有的位能(pe)會在當物體通這一點equilibrium position 時全部變成動能(ke),但是加速度d2x/dt2會和dx/dt (v)的方向相反即d2x/dt2 +ve時,dx/dt (v)會時 -ve. 但你說的amplitude,考你的時候會說明是max.amplitude or half of its max. amplitude or amplitude at particular timing.

咁個maximum displacement position係唔係唔等於amplitude?,

答:maximum displacement position係等於 MAX. amplitude唔等於amplitude.咁代表甚麼?它代表物體去到maximum displacement position所走的全路程,也可以用來計算出走(1/2)半路程所須的時間.計法如下.

先想像物體由maximum displacement position去半路程(half of its max. amplitude )

let A&#39; be displacement position varies with (wt), Ao be initial displacement and A/2 be the half of the displacement position. In addition Q is intial phase angle. due to

A&#39; = Aosin(wt+Q) and initial phase angle is 0

A = Aosin(wt)

due to Ao = A max.displacement position ,then A/2 = Asin(wt) [A/2代入A&#39;]

1/2 = sin(wt) wt = 30degree. Since I don&#39;t have a calculator, I can&#39;t find value in radian.

when (wt) is know. the value of time can be found by 2*3.1415*f*t is frequency is known.

w = 2*pi/T (T is period) = 2*pi*f

I hope you can understand what I am talking about.

2007-01-15 16:41:14 補充：

如果想更深入地了解shm,留意星期日的早上的明珠台的Open U節目, 有一個叫鐘擺的節目,入面有個機械工程的Dr.做題目及解釋為何這樣計,上星期日他用了limit來計如果個鐘擺條string長了一些會怎樣,他plot了個圖出來.學好shm, 對之後學alternating current(AC)也有幫助

2007-01-15 17:08:31 補充：

我希望你參考一下95-99年(我忘記了那一年)的一條shm,是一個小物體放在一個你盘上,而個盘連住條彈簧,這條shm好毒,小心做,毒就毒在gravitational PE is taken into account.看看marking scheme如何做,必有得着

2007-01-19 16:02:19 補充：

According to physics some text books such as further phy. and Tom Duncan phy, they tend to make equilibrium position 等於amplitude即只是用amplitude一字就表示max amplitude. When they mention amplitude, they means equilibrium position

• equilirium posittion is completely different from the amplitude....

At eqm position

the speed of the particle is max

the acceleration and displacement of the particle is zero

At max displacement

v=0

KE =0

PE =max

==&gt;it is the position at representing the amplitude of oscillation