Question

質(zhì)點(diǎn)沿x軸做簡(jiǎn)諧運(yùn)動(dòng)，平衡位置為坐標(biāo)原點(diǎn)O，質(zhì)點(diǎn)經(jīng)過(guò)a點(diǎn)（x_a="-5" cm）和b點(diǎn)（x_b="5" cm）時(shí)速度相同，所用時(shí)間t_ab="0.2" s,質(zhì)點(diǎn)由b回到a點(diǎn)所用最短時(shí)間t_ba="0.4" s，則該質(zhì)點(diǎn)做簡(jiǎn)諧運(yùn)動(dòng)的頻率為（   ）

A．1 Hz

B．1.25 Hz

C．2 Hz

D．2.5 Hz

Answer 1

B

本題考查簡(jiǎn)諧運(yùn)動(dòng)的周期和頻率概念，充分利用簡(jiǎn)諧運(yùn)動(dòng)的對(duì)稱(chēng)性是解題關(guān)鍵.
設(shè)質(zhì)點(diǎn)在AA′間運(yùn)動(dòng)，O為平衡位置，t_Aa=t₁,t_aO=t₂，如圖1所示.

圖1
情形1：計(jì)時(shí)時(shí)刻質(zhì)點(diǎn)從a點(diǎn)沿x軸正向運(yùn)動(dòng)，
則2t₂="0.2" s                                                                   ①
2t₁+2t₂="0.4" s                                                                   ②
又T=4(t₁+t₂)                                                                  ③
                                                                      ④
解①②③④得f="1.25" Hz.
情形2：計(jì)時(shí)時(shí)刻質(zhì)點(diǎn)從a點(diǎn)沿x軸負(fù)向運(yùn)動(dòng)，
則4t₁+2t₂="0.2" s
2t₂="0.4" s
顯然上述情形不成立.
綜上所述，答案為B.