Physics Exam4

The displacement is given by the function

圖片參考：http://upload.wikimedia.org/math/7/a/c/7ac3484c2b42686da65e26d84c792894.png

We then differentiate once to get an expression for the velocity at any time.

圖片參考：http://upload.wikimedia.org/math/f/c/d/fcd0e5911ca23e8d4642647d8106d340.png

And once again to get the acceleration at a given time.

圖片參考：http://upload.wikimedia.org/math/c/c/8/cc8db2e97f088a95810e52488cd18560.png

These results can of course be simplified, giving us an expression for acceleration in terms of displacement.

圖片參考：http://upload.wikimedia.org/math/6/0/3/603d83916e2771ef99de50a13bce1173.png

SO
the maximum acceleration of the needle
=(2*PI*2.55)^2*1.27
=326 cm/s2
答案是C

Using max. acceleration = -w^2 x A where
w = angular frequency = 2兀f
A = amplitude of s.h.m.

w = 2兀 x 2.55 = 16.02 rad/s
A = 1.27 cm

Hence max. acc = (16.02)^2 x 1.27 = 326 cm/s^2

Answer: C