Основы измерений. Долгополов В.Т. - 6 стр.

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МФТИ | Москва

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ihemqZ_l hiihabpbx \ ebp_ Z\lhjh\ b ijb\_j`_gp_\ l_hjbb. <k_ __ ^Zggu_ b \u\h^u
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bkke_^h\Zl_eyfb.
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[he__ lsZl_evguo bkke_^h\Zgbc, [he__ \ukhdhc d\ZebnbdZpbb bkke_^h\Zl_ey b
hij_^_e_gghc hl\Z]b, gZdhg_p.
4. Qlh lZdh_ «baf_j_gb_» b dZdb_ baf_j_gby [u\Zxl.
>ey ijh\_^_gby ex[h]h wdki_jbf_glZ gm`gh, \h-i_j\uo, hij_^_eblv nbabq_kdb_
\_ebqbgu, \h-\lhjuo, mf_lv bo baf_jblv. Ihkdhevdm ex[Zy nbabq_kdZy \_ebqbgZ aZ^Z_lky
kihkh[hf __ baf_j_gby, \ kmsghklb, g_h[oh^bfh lhevdh mf_gb_ b ZiiZjZlmjZ ^ey
baf_j_gbc. < ke_^mxsbo ]eZ\Zo dmjkZ fu jZkkfhljbf \hijhku, k\yaZggu_ k baf_j_gb_f
nbabq_kdbo \_ebqbg [he__ ih^jh[gh.
GZb\gh dZ`_lky, qlh baf_j_gb_ – wlh kjZ\g_gb_ bkke_^m_fh]h l_eZ,
oZjZdl_jbklbdb, \_ebqbgu k wlZehghf. GZ kZfhf ^_e_, wlh [he__ h[sbc ijhp_kk.
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we_f_glu Z[kljZdlgh]h \hh[jZ`Z_fh]h fgh`_kl\Z, hkms_kl\ey_fh_ ih hij_^_e_gguf
ijZ\beZf ij_h[jZah\Zgby. Khhlghr_gby, kms_kl\mxsb_ f_`^m we_f_glZfb bkoh^gh]h
fgh`_kl\Z, ^he`gu khojZgylvky b \ \hh[jZ`Z_fhf fgh`_kl\_. GZijbf_j, ^\Z we_f_glZ
fh]ml [ulv wd\b\Ze_glgu beb g_wd\b\Ze_glgu. DZd ijZ\beh, ijhkljZgkl\h h[jZah\ g_
y\ey_lky _^bgkl\_gguf, lh _klv hlh[jZ`_gb_ fh`_l [ulv ih «aZdhgguf» ijZ\beZf
i_j_g_k_gh gZ ^jm]h_ fgh`_kl\h h[jZah\. Ijhkl_crbf ijbf_jhf lZdhc hi_jZpbb
y\ey_lky kf_gZ fZkrlZ[Z \ baf_j_gbyo.
<k_ \hafh`gu_ baf_j_gby jZa[b\Zxlky gZ g_kdhevdh ]jmii.
(1) GhfbgZevgh_ baf_j_gb_.
?keb baf_jyxlky we_f_glu fgh`_kl\Z S, lh baf_jbl_evgZy kbkl_fZ ^he`gZ [ulv kihkh[gZ
hij_^_eblv s
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. >himklbfh_ ij_h[jZah\Zgb_ fgh`_kl\Z j_amevlZlh\
baf_j_gbc hkms_kl\ey_lky \aZbfgh-h^ghagZqguf ij_h[jZah\Zgb_f. g(i
1
)=g(i
2
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1
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[hlZgbdb b [bheh]bb, dZd jZa^_e_gb_ ih deZkkZf, hljy^Zf b l.^.
Ijbf_j ghfbgZevgh]h baf_j_gby. DZdhc kbf\he a^_kv ebrgbc?
E , D,
R,
4, N, u, T
(2) Ihjy^dh\h_ baf_j_gb_.
s
1
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2
. >himklbfh_ ij_h[jZah\Zgb_ hkms_kl\ey_lky ijhba\hevghc fhghlhggh
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1
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2
), _keb i
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. Baf_j_gb_ lZdh]h
lbiZ ijhba\h^yl, gZijbf_j, khe^Zlu ijb ihkljh_gbb ih jhklm.
(3) Bgl_j\Zevgh_ baf_j_gb_.
< bgl_j\Zevghf baf_j_gbb ihfbfh mkeh\by s
1
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|. >himklbfh_ ij_h[jZah\Zgb_ hkms_kl\ey_lky ebg_cgh
\hajZklZxs_c nmgdpb_c g(i) = mi +n, m>0. Ijbf_jhf bgl_j\Zevgh]h baf_j_gby y\ey_lky
baf_j_gb_ l_fi_jZlmju ih P_evkbx beb NZj_g]_clm.
(4) IjhihjpbhgZevgh_ baf_j_gb_.
s
1
>ms
2
beb s
1
< ms
2
. >himklbfh_ ij_h[jZah\Zgb_ k ihfhsvx nmgdpbc \b^Z g(i) = mi, m>0. 
ijh\_jy\r_cky l_hjbb [m^_l gZc^_g dZdhc-eb[h ^_n_dl, _keb hgZ hdZ`_lky g_iheghc beb
hrb[hqghc.
      Kh\_jr_ggh ^jm]Zy kblmZpby k im[ebdZpb_c, hijh\_j]Zxs_c l_hjbx. HgZ kjZam `_
ihemqZ_l hiihabpbx \ ebp_ Z\lhjh\ b ijb\_j`_gp_\ l_hjbb. ey ijh\_^_gby ex[h]h wdki_jbf_glZ gm`gh, \h-i_j\uo, hij_^_eblv nbabq_kdb_
\_ebqbgu, \h-\lhjuo, mf_lv bo baf_jblv. Ihkdhevdm ex[Zy nbabq_kdZy \_ebqbgZ aZ^Z_lky
kihkh[hf __ baf_j_gby, \ kmsghklb,      g_h[oh^bfh lhevdh mf_gb_ b ZiiZjZlmjZ ^ey
baf_j_gbc. < ke_^mxsbo ]eZ\Zo dmjkZ fu jZkkfhljbf \hijhku, k\yaZggu_ k baf_j_gb_f
nbabq_kdbo \_ebqbg [he__ ih^jh[gh.
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oZjZdl_jbklbdb, \_ebqbgu k wlZehghf. GZ kZfhf ^_e_, wlh [he__ h[sbc ijhp_kk.
Hij_^_ebf baf_j_gb_ dZd hlh[jZ`_gb_ we_f_glh\         wfibjbq_kdh]h fgh`_kl\Z gZ
we_f_glu Z[kljZdlgh]h \hh[jZ`Z_fh]h fgh`_kl\Z, hkms_kl\ey_fh_ ih hij_^_e_gguf
ijZ\beZf ij_h[jZah\Zgby. Khhlghr_gby, kms_kl\mxsb_ f_`^m we_f_glZfb bkoh^gh]h
fgh`_kl\Z, ^he`gu khojZgylvky b \ \hh[jZ`Z_fhf fgh`_kl\_. GZijbf_j, ^\Z we_f_glZ
fh]ml [ulv wd\b\Ze_glgu beb g_wd\b\Ze_glgu. DZd ijZ\beh, ijhkljZgkl\h h[jZah\ g_
y\ey_lky _^bgkl\_gguf, lh _klv hlh[jZ`_gb_ fh`_l [ulv ih «aZdhgguf» ijZ\beZf
i_j_g_k_gh gZ ^jm]h_ fgh`_kl\h h[jZah\. Ijhkl_crbf ijbf_jhf lZdhc hi_jZpbb
y\ey_lky kf_gZ fZkrlZ[Z \ baf_j_gbyo.
      himklbfh_ ij_h[jZah\Zgb_ fgh`_kl\Z j_amevlZlh\
baf_j_gbc hkms_kl\ey_lky \aZbfgh-h^ghagZqguf ij_h[jZah\Zgb_f. g(i1)=g(i2), _keb i1=i2,
b g(i1)zg(i2), _keb i1zi2. Ijbf_ju ghfbgZevguo baf_j_gbc gZf ohjhrh ba\_klgu ba
[hlZgbdb b [bheh]bb, dZd jZa^_e_gb_ ih deZkkZf, hljy^Zf b l.^.

Ijbf_j ghfbgZevgh]h baf_j_gby. DZdhc kbf\he a^_kv ebrgbc?
E , D, R, 4, N, u, T
       (2) Ihjy^dh\h_ baf_j_gb_.
s1>s2 beb s1< s2. >himklbfh_ ij_h[jZah\Zgb_ hkms_kl\ey_lky ijhba\hevghc fhghlhggh
\hajZklZxs_c nmgdpb_c g(i1)>g(i2), _keb i1>i2, b g(i1)< g(i2), _keb i1< i2. Baf_j_gb_ lZdh]h
lbiZ ijhba\h^yl, gZijbf_j, khe^Zlu ijb ihkljh_gbb ih jhklm.

    (3) Bgl_j\Zevgh_ baf_j_gb_.
< bgl_j\Zevghf baf_j_gbb ihfbfh mkeh\by s1 >s2 beb s1 < s2 ^he`gh [ulv \uiheg_gh |s1-
s2|>|s3-s4| beb |s1-s2| < |s3-s4|. >himklbfh_ ij_h[jZah\Zgb_ hkms_kl\ey_lky ebg_cgh
\hajZklZxs_c nmgdpb_c g(i) = mi +n, m>0. Ijbf_jhf bgl_j\Zevgh]h baf_j_gby y\ey_lky
baf_j_gb_ l_fi_jZlmju ih P_evkbx beb NZj_g]_clm.

 (4) IjhihjpbhgZevgh_ baf_j_gb_.
s1>ms2 beb s1 < ms2 . >himklbfh_ ij_h[jZah\Zgb_ k ihfhsvx nmgdpbc \b^Z g(i) = mi, m>0.

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