Основы измерений. Долгополов В.Т. - 22 стр.

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МФТИ | Москва

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a d
2
y/dt
2
+ bdy/dt +y =x(t).
Ih^h[gu_ kbkl_fu ohjhrh gZf ba\_klgu ih kemqZx [Zeebklbq_kdh]h ]Zev\Zghf_ljZ.
I_j_oh^gu_ oZjZdl_jbklbdb lZdbo kbkl_f ijb jZaebqguo agZq_gbyo hlghkbl_evgh]h
dhwnnbpb_glZ aZlmoZgby z= b/(2a
1/2
) ihdZaZgu gZ jbkmgd_ 18.
Jbk 18, Z
=a
-1/2
.
G_ebg_cgu_ kbkl_fu hibku\Zxlky g_ebg_cgufb bgl_]jh-^bn_j_gpbZevgufb
mjZ\g_gbyfb. Bkihevah\Zgb_ lZdbo kbkl_f ^ey baf_j_gbc g_`_eZl_evgh.
13. H[jZlgh_ \ebygb_ baf_jbl_evghc kbkl_fu gZ baf_jy_fuc h[t_dl:
kh]eZkh\Zgb_.
Baf_jbl_evgZy kbkl_fZ, ^ey lh]h, qlh[u ihemqblv bgnhjfZpbx h[ baf_jy_fhf
h[t_dl_, eb[h hl[bjZ_l m g_]h qZklv wg_j]bb, eb[h, gZh[hjhl, \\h^bl ba[ulhqgmx wg_j]bx
b bkke_^m_l hldebd h[t_dlZ. B \ lhf b \ ^jm]hf kemqZ_ kbkl_fZ \hafmsZ_l baf_jy_fuc
h[t_dl, qlh ijb\h^bl d hrb[dZf \ baf_j_gbb. >ey mf_gvr_gby wlh]h \ebygby beb ^ey
^hklb`_gby fZdkbfZevghc qm\kl\bl_evghklb \u]h^gh ki_pbZevguf h[jZahf ih^kljhblv
\oh^ghc dZkdZ^ baf_jbl_evghc kbkl_fu, dZd ]h\hjyl, ijhba\_klb kh]eZkh\Zgb_.
:gwg_j]_lbq_kdh_ kh]eZkh\Zgb_.
?keb klj_fblvky d fbgbfZevghfm \hafms_gbx baf_jy_fh]h h[t_dlZ, lh
g_h[oh^bfh h[_ki_qblv fbgbfZevguc h[f_g wg_j]b_c f_`^m baf_jy_fuf h[t_dlhf b
baf_jbl_evghc kbkl_fhc, l._. Zgwg_j]_lbq_kdh_ kh]eZkh\Zgb_. >ey Zg_j]_lbq_kdh]h
kh]eZkh\Zgby ijb baf_j_gbb gZijy`_gby, gZijbf_j, gm`gh k^_eZlv \gmlj_gg__
khijhlb\e_gb_ \hevlf_ljZ fZdkbfZevgh [hevrbf, Z ijb baf_j_gbb lhdZ –\gmlj_gg__
khijhlb\e_gb_ Zfi_jf_ljZ fbgbfZevguf.
Wg_j]_lbq_kdh_ kh]eZkh\Zgb_.
Ijbf_gy_lky ^ey ba\e_q_gby ba baf_jy_fh]h h[t_dlZ fZdkbfZevgh \hafh`ghc
fhsghklb. (Djblbqgh \ kemqZ_ bkihevah\Zgby iZkkb\guo baf_jbl_evguo kbkl_f, l._.
kbkl_f , \ dhlhjuo g_l mkbe_gby fhsghklb.) JZkkfhljbf \ dZq_kl\_ ijbf_jZ ko_fm,
Jbk. 19 . 
                             a d2y/dt2 + bdy/dt +y =x(t).
Ih^h[gu_ kbkl_fu ohjhrh gZf ba\_klgu ih kemqZx [Zeebklbq_kdh]h ]Zev\Zghf_ljZ.
I_j_oh^gu_ oZjZdl_jbklbdb lZdbo kbkl_f ijb jZaebqguo agZq_gbyo hlghkbl_evgh]h
dhwnnbpb_glZ aZlmoZgby z= b/(2a1/2) ihdZaZgu gZ jbkmgd_ 18.




                                  Jbk 18, Z =a-1/2.
G_ebg_cgu_ kbkl_fu         hibku\Zxlky g_ebg_cgufb bgl_]jh-^bn_j_gpbZevgufb
mjZ\g_gbyfb. Bkihevah\Zgb_ lZdbo kbkl_f ^ey baf_j_gbc g_`_eZl_evgh.

 13. H[jZlgh_ \ebygb_ baf_jbl_evghc kbkl_fu gZ baf_jy_fuc h[t_dl:
                           kh]eZkh\Zgb_.
      Baf_jbl_evgZy kbkl_fZ, ^ey lh]h, qlh[u ihemqblv bgnhjfZpbx h[ baf_jy_fhf
h[t_dl_, eb[h hl[bjZ_l m g_]h qZklv wg_j]bb, eb[h, gZh[hjhl, \\h^bl ba[ulhqgmx wg_j]bx
b bkke_^m_l hldebd h[t_dlZ. B \ lhf b \ ^jm]hf kemqZ_ kbkl_fZ \hafmsZ_l baf_jy_fuc
h[t_dl, qlh ijb\h^bl d hrb[dZf \ baf_j_gbb. >ey mf_gvr_gby wlh]h \ebygby beb ^ey
^hklb`_gby fZdkbfZevghc qm\kl\bl_evghklb \u]h^gh ki_pbZevguf h[jZahf ih^kljhblv
\oh^ghc dZkdZ^ baf_jbl_evghc kbkl_fu, dZd ]h\hjyl, ijhba\_klb kh]eZkh\Zgb_.
      :gwg_j]_lbq_kdh_ kh]eZkh\Zgb_.
      ?keb klj_fblvky d fbgbfZevghfm \hafms_gbx                baf_jy_fh]h h[t_dlZ, lh
g_h[oh^bfh h[_ki_qblv fbgbfZevguc h[f_g wg_j]b_c f_`^m baf_jy_fuf h[t_dlhf b
baf_jbl_evghc kbkl_fhc, l._. Zgwg_j]_lbq_kdh_ kh]eZkh\Zgb_. >ey Zg_j]_lbq_kdh]h
kh]eZkh\Zgby ijb baf_j_gbb gZijy`_gby, gZijbf_j, gm`gh k^_eZlv \gmlj_gg__
khijhlb\e_gb_ \hevlf_ljZ fZdkbfZevgh [hevrbf, Z ijb baf_j_gbb lhdZ –\gmlj_gg__
khijhlb\e_gb_ Zfi_jf_ljZ fbgbfZevguf.
       Wg_j]_lbq_kdh_ kh]eZkh\Zgb_.
      Ijbf_gy_lky ^ey ba\e_q_gby ba baf_jy_fh]h h[t_dlZ fZdkbfZevgh \hafh`ghc
fhsghklb. (Djblbqgh \ kemqZ_ bkihevah\Zgby iZkkb\guo baf_jbl_evguo kbkl_f, l._.
kbkl_f , \ dhlhjuo g_l mkbe_gby fhsghklb.) JZkkfhljbf \ dZq_kl\_ ijbf_jZ ko_fm,




                                                                 Jbk. 19 .

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