H U O N G D A N H O C S I N H S O D U N G D U O N G T R O N L U Q N G G I A C G I A I B A I T A P DAO DONG DIEU HOA M O N V A T U
O ThS. NGUYEN LAM SUNG*
1. Su dung duong tron lugng giac gidi bdi todn dao dong dieu hda (DDDH)
DDDH Id dao ddng tuan hodn md li do duqc md td dudi dqng X = Asinfeot +cp) hoqc X = Acos(cot +cp), trong dd: A, co, cp Id hdng sd (A, co > 0).
Chang hqn, dao ddng cua con lac Id xo, dao ddng cua con lac don, con lac Vdt li vdi gdc lech nhd Id cdc DDDH.
Trong qud trinh day hqc Vdt li d trudng trung hqc phd' thdng, gido vien (GV) cd the hudng ddn hqc sinh (HS) su dyng cdc cdch khdc nhau nhu:
dung dudng tron lugng gidc, bien ddi lugng gidc, bien ddi dqi sd, dung vecto quay,... de gidi cdc bdi todn DDDH. Trong dd, GV can chu trqng hudng ddn HS luyen tap kT ndng dung dudng tron luqng gidc gidi bdi todn DDDH theo cdc budc: 1) Xdy dyng md hinh todn hqc; 2) Xu li md hinh todn hqc; 3) Phdn tich vd ket ludn ve ket qud.
O budc 1, hudng ddn HS xdy dyng md hinh todn hqc, chu y nhung diem sau: 1) GV giup HS hieu rd ban chdt mdi quan he giua chuyen ddng tron deu vd DDDH, coi DDDH Id hinh chieu cua mdt chuyen ddng tron deu tren true tqa dd trong mat phdng quy dao. GV cd the minh hoa (neu ket hqp su dyng video clip thi hieu qud se rat td't) dieu ndy cho HS khi dua ra vi dy: Mdt chdt diem chuyen ddng tron deu vdi van tdc gdc co tren quy dao tron ban kinh R theo chieu nguqc kim dong hd. Tqi thdi diem t = 0, chdt diem d vj tri MQ, ban kinh vecta OM„ hqp vdi true OX mdt gdc cp. Sau t gidy, chdt diem den vi tri M vd ban kinh vecta OM quay duqc gdc Id cot (hinh 1). HS de ddng nhdn thd'y, hinh chieu cua OM tren true OX hoqc OY deu bieu dien dudi dqng DDDH X = A cos (cot + cp) hoqc X = A sin (cot + cp); 2) Hudng ddn HS: + Ve dudng tron ban kinh bdng bien dd A cua dao ddng, he true tqa dd di qua tdm dudng tron. True OX ndm ngang hudng sang phdi, true OY thdng dung hudng len; + Neu dao ddng cd phuang trinh X = A cos (cot + cp), ta chqn true li dd Tap chi Giao due so 252 (ki 2 - 12/2010)
Id true OX, true vdn tdc md td theo chieu dm Id true OY; + Neu dao ddng cd phuang trinh X = Asinfcot + cp), ta chqn true li dd dao ddng md td theo chieu duang true OY, true van tdc duqc md td theo chieu duong cua true OX.
O buoc 2, hudng ddn cho HS xu li md hinh todn hqc: 1) HS dya vdo gid thiet bdi todn, xdc djnh vj tri cua chd't diem tuang ung tren dudng tron. TCrdd, xdc djnh pha ban ddu cua dao ddng:
+ Neu bdi todn cho thdi diem ban ddu t = 0, cp chinh Id gdc tqo bdi ban kinh vecta d thdi diem t = 0 vdi chieu duang cua true OX; + Neu bdi todn cho d thdi diem bdt ki t * 0, ta quay tu vj tri cd t * 0 vdi chieu cung chieu kim ddng hd — vdng.
Khi dd, den vi tri cd thdi diem t = 0, HS d i ddng xdc djnh duqc gdc cp tuong ty nhu tren; 2) Hudng ddn HS van dyng phep chieu len cdc true tqa do, tim qudng dudng md vdt di duqc trong mdt khodng thdi gian ndo dd; 3) HS xdc djnh gdc a, tinh duqc cdc dqi luqng co, At theo cdng thuc co = — khi biet vj tri ciia vdt tqi 2 thdi diem; 4) Tap luyen cho HS quan sat linh hoqt cdc tam gidc ve duqc sau khi thyc hien phep chieu len cdc true tqa dd tu vi tri cua chd't diem tren dudng tron (giup cdc em cd the xdc djnh duqc nhieu thdng sd khdc cua DDDH, dqc biet Id viet phuang trinh dao dqng cua vdt).
Obudc 3: Hudng ddn HS phdn tich, ket ludn ve ket qud, chu y kiem tra ket qud tim duqc d budc 2 vd lya chqn cdu trd Idi phu hqp vdi yeu cdu bdi todn.
2. Mot sd vi dy
Vidy 7: Mdt mqch dao ddng dien tu li tudng, cd dao ddng dien tu ty do. Tqi thdi diem t = 0, dien tich tren mdt ban ty dqt eye dqi. Sau khodng thdi gian ngdn nhdt t, dien tich tren ban ty bdng mdt nua gid trj eye dqi. Khi dd, chu ki dao ddng
* Truong Cao dang su pham Quang Ninn
rieng cua mach dao dong nay la: A) 4At; B) 6At;
C) 3At; D) 12At.
Huong dan:
Budc 1: Xay dung mo hinh toan hoc, HS can chu y nhung diem sau: - Coi dien tich nhu mot chdt di em DDDH; - Xac dinh dao dong dien tich trong mqch co dqng q = QQcos(cot + cp), chu ki dao dqng rieng tinh theo cong thuc T = Ve duang tron ban kinh QQ, xac dinh vi tri tqi t = 0 cua dien tich tren duang tron (hinh 1).
Budc 2: Xu li mo hinh toan hqc. Tu diem bieu dien gia trj, HS ke duang thang vuong goc voi true dien tich va xac dinh vj tri cua dien tich tren duang tron d thdi diem gdn nhdt de dat duoc &
2 HS cdn Hinh 1
ndm duqc dien tich dao ddng mdt chu ki tuong ung vdi ban kinh vecto quay duqc 1 vdng; d ddy, ban kinh vec to quay duqc mdt gdc Id a = —.
Budc 3: Phdn tich vd ket ludn ve ket qud. HS ket ludn: Chu ki dao ddng cua dien tich Id dAt (dap an B).
Vidy 2: Mdt vqt DDDH cd li dd X = 2cos(cot + cp).
Tim qudng dudng Idn nhdt md vqt di duqc sau T
khodng thdi gian Id — (T Id chu ki dao ddng cua vdt). Chqn dap an dung: A) 1; B) 2;C) 4;D)2V2.
Hudng dan:
Budc 1: HS xdc djnh duqc A = 2, ve dudng tron ban kinh bdng 2 vd ndm vung: khi vdt cd vi tri gdn v| tri cdn bang thi van tdc cdng Idn. Tu dd, xdc djnh vdt se di duqc qudng dudng Idn nhdt khi nd dao ddng 2 ben v| tri cdn bdng (do tinh chdt ddi xung - hinh 2).
Budc 2: HS hieu rd mdt chu ki dao ddng tuong ung vdi ban kinh vecta quay 1 vdng (2TT). TU dd, dua ra ket ludn vdi thdi gian —, ban T kinh vecto se quay mdt gdc 1
la T"
Budc 3. Chqn dap an D.
Vi dy 3: Ddt mot hieu dien the xoay chieu u = 220^2 sinlOCkt (V) vdo hai cue cua mdt den dng. Den chi sdng khi dien dp dqt vdo 2 cue cua den Id 1IOV2 (V). Hay tinh ti so giua thdi gian sdng vd thdi gian tdi cua den trong nua chu ki cua ddng dien khi qua den. Chqn dap an dung:
A)±;B)l;C)f;D)2.
Huong ddn:
Budc 1: HS can xdc djnh duqc A = 220 V2 vd ve dudng tron ban kinh 220 V2 (hinh 3). Chqn true
bieu dien gid tri hieu dien the u Id true rung.
Budc 2: HS xdc djnh thdi gian den sdng thi ban kinh Hinh 3 vecta quay mdt gdc Id ,
thdi gian den tdi thi ban kinh vecta quay duqc gdc Id —. Tinh duqc ti sd cdn tim Id 2.
Budc 3: Chqn dap an D.
3. Gidi thieu mot so bdi tap
Bdi, 1: Mdt vqt DDDH cd tdn'sd 2 Hz, bien dd 4cm. O thdi diem ndo dd, vqt chuyen ddng theo chieu dm qua vj tri cd li do 2cm thi sau 1/12 s vqt chuyen ddng theo: A) Chieu dm qua vj tri cd li dd -2V3cm; B) Chieu dm qua vi tri cdn bdng;
C) Chieu duang qua vi tri cd li dd - 2cm; D) Chieu dm qua vi tri cd li dd - 2cm.
Hudng dan : dap an B).
Bdi 2: Mdt vdt DDDH vdi phuong trinh x = Acos(^ + ^) cm. Sau thdi gian — ke tu thdi
-vd tinh duqc (dya
vao tam gidc vudng) qudng dudng Id 2 V2 .
diem ban ddu vqt di duqc qudng dudng 10cm.
Bien dd dao ddng ciia vdt Id: A) 30/7 cm; B) dem; C) 4cm; D) 5cm.
Hudng dan: dap an C).Q Tai lieu tham khao
1. Tran Dire Chien. "Ren luyen nang lire van dung kien thuc vao thuc tien cho sinh vien trong day hpc toan d trudng Cao dang su pham Quang Ninh". Du an trung hpc co sd, 2007.
2. Nguyen The" Khai (tdng chu bien) - Vu Thanh Khie"t (chu bien). Vat li 12 (nang cao). NXB Gido due, H. 2007.
3. NguySn The Khoi - Vu Thanh Khiet (d6ng chu bien).
Bai tap Vat li 12 (nang cao). NXB Gido due, H. 2007.
Tap chi Giao due so 252 (ki a -1 a/2010)
