? 發問於 教育及參考書標準及測試 · 1 十年前

# phy shm!!![10分]

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

### 2 個解答

• 莫愁
Lv 6
1 十年前
最愛解答

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

• 1 十年前

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