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Sebuah partikel melakukan GHS dengan amplitudo 2 cm dan periode 3 detik. Jika mula-mula simpangan partikel sama dengan nol, berapa simpangan partikel itu setelah 4 1 ​ , 2 1 ​ , 1 , 1 2 1 ​ , dan 2 4 3 ​ detik? Hitung pula kecepatannya pada saat tersebut!

Sebuah partikel melakukan GHS dengan amplitudo 2 cm dan periode 3 detik. Jika mula-mula simpangan partikel sama dengan nol, berapa simpangan partikel itu setelah  detik? Hitung pula kecepatannya pada saat tersebut!space 

  1. ...space 

  2. ...space 

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R. Sobirin

Master Teacher

Mahasiswa/Alumni Universitas Indonesia

Jawaban terverifikasi

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Pembahasan

Kecepatan sudut: Persamaan simpangan dalam cm: Saat : Saat : Saat : Saat : Saat : Persamaan kecepatan: Saat : Saat : Saat : Saat : Saat :

Kecepatan sudut:

omega equals fraction numerator 2 pi over denominator T end fraction equals fraction numerator 2 pi over denominator 3 end fraction space rad divided by straight s 

Persamaan simpangan dalam cm:

y equals A sin open parentheses omega t close parentheses y equals 2 sin open parentheses fraction numerator 2 pi over denominator 3 end fraction t close parentheses  

Saat t equals 1 fourth space detik:

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 sin open parentheses fraction numerator 2 pi over denominator 3 end fraction.1 fourth close parentheses end cell row blank equals cell 2 sin open parentheses pi over 6 close parentheses end cell row blank equals cell 2.0 comma 5 end cell row blank equals cell 1 space cm end cell end table 

Saat t equals 1 half space detik

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 sin open parentheses fraction numerator 2 pi over denominator 3 end fraction.1 half close parentheses end cell row blank equals cell 2 sin open parentheses pi over 3 close parentheses end cell row blank equals cell 2.1 half square root of 3 end cell row blank equals cell square root of 3 space cm end cell end table  

Saat t equals 1 space detik

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 sin open parentheses fraction numerator 2 pi over denominator 3 end fraction.1 close parentheses end cell row blank equals cell 2 sin open parentheses fraction numerator 2 pi over denominator 3 end fraction close parentheses end cell row blank equals cell 2.1 half square root of 3 end cell row blank equals cell square root of 3 space cm end cell end table 

Saat t equals 3 over 2 space detik

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 sin open parentheses fraction numerator 2 pi over denominator 3 end fraction.3 over 2 close parentheses end cell row blank equals cell 2 sin open parentheses pi close parentheses end cell row blank equals cell 2.0 end cell row blank equals cell 0 space cm end cell end table 

Saat t equals 11 over 4 space detik

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 sin open parentheses fraction numerator 2 pi over denominator 3 end fraction.11 over 4 close parentheses end cell row blank equals cell 2 sin open parentheses fraction numerator 11 pi over denominator 6 end fraction close parentheses end cell row blank equals cell 2. open parentheses negative 0 comma 5 close parentheses end cell row blank equals cell negative 1 space cm end cell end table 

Persamaan kecepatan:

v equals fraction numerator d y over denominator d t end fraction equals fraction numerator 4 pi over denominator 3 end fraction cos open parentheses fraction numerator 2 pi over denominator 3 end fraction t close parentheses  

Saat t equals 1 fourth space detik:

table attributes columnalign right center left columnspacing 0px end attributes row v equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses fraction numerator 2 pi over denominator 3 end fraction.1 fourth close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses pi over 6 close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction. fraction numerator square root of 3 over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 3 pi over denominator 3 end fraction space cm divided by straight s end cell end table   

Saat t equals 1 half space detik

table attributes columnalign right center left columnspacing 0px end attributes row v equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses fraction numerator 2 pi over denominator 3 end fraction.1 half close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses pi over 3 close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction.1 half end cell row blank equals cell fraction numerator 2 pi over denominator 3 end fraction space cm divided by straight s end cell end table    

Saat t equals 1 space detik

table attributes columnalign right center left columnspacing 0px end attributes row v equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses fraction numerator 2 pi over denominator 3 end fraction.1 close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses fraction numerator 2 pi over denominator 3 end fraction close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction. open parentheses negative 1 half close parentheses end cell row blank equals cell negative fraction numerator 2 pi over denominator 3 end fraction space cm divided by straight s end cell end table 

Saat t equals 3 over 2 space detik

table attributes columnalign right center left columnspacing 0px end attributes row v equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses fraction numerator 2 pi over denominator 3 end fraction.3 over 2 close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses pi close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction. open parentheses negative 1 close parentheses end cell row blank equals cell negative fraction numerator 4 pi over denominator 3 end fraction space cm divided by straight s end cell end table  

Saat t equals 11 over 4 space detik

table attributes columnalign right center left columnspacing 0px end attributes row v equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses fraction numerator 2 pi over denominator 3 end fraction.11 over 4 close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction cos open parentheses fraction numerator 11 pi over denominator 6 end fraction close parentheses end cell row blank equals cell fraction numerator 4 pi over denominator 3 end fraction. fraction numerator square root of 3 over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 3 pi over denominator 3 end fraction space cm divided by straight s end cell end table 

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