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[問題] SHM問題

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SHM問題

DSE學生無聊得滯自修AL phy

A block of mass m is attached to two identical spring as shown. The force constant of each spring is k.If the block is made to execute simple harmonic motion, the period will be
A. 2pi sqrt (m/2k)
B. 2pi sprt (2m/k)
C. 2pi sqrt (k/2m)
D. 2pi sqrt (2k/m)

點解係B唔係A?
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k_eq=(k^-1+k^-1)^-1=k/2
w=sqrt(k/m)=sqrt(k/2m)
T=2pi/w=2pi sqrt(2m/k)
spring:
series(k1^-1+k2^-1)^-1
parallel:k1+k2

[ 本帖最後由 hinokari 於 2012-5-2 06:33 PM 編輯 ]

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thx

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補充一下証明方式
in series:

T=k1x1=k2x2

x=x1+x2=T/k1+T/k2

as x=T/k(eq)

so1/k(eq)=1/k1+1/k2

parallel用相同concept可證

SHM係物理黎講好重要

加油啊~

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將Spring 分成n 段,then k --> n*k
路曼曼其脩遠兮 吾將上下而求索

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明晒

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A block of mass placed on a vertical light spring is in static equilibrium at level O as shown in (a).
When the mass is raised to level P and is released from rest, it would hit the spring at Q as shown in (b) and the lowest position that the block would reach is at R as shown in (c).
Neglecting air resistance and considering the motion of the block from P to R, which of the following statements is/are true?
(1) The speed of the block is at a maximum when it is at Q.
(2) It is always true that PQ>QR.
(3) The resultant force acting on the block when it is at R may be greater than its weight.
答案係(3) only. 唔識點睇.

[ 本帖最後由 分身ac 於 2012-5-2 09:10 PM 編輯 ]
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(1)由P至Q,最快當然是Q
由block掂到spring開始就係SHM
所以只需要考慮SHM最快係邊就得


(2)conservation of energy

P.E.at P =e.P.E.at R

會發現PQ與QR的關係

(3)resultant force at amplitude = mw^2A

可以調整A令net force大過mg

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