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

解析:

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.