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Salah satu ujung seutas tali panjang digetarkan de...

Salah satu ujung seutas tali panjang digetarkan dengan frekuensi 5 Hz dan amplitudo 8 cm sehingga gelombang merambat pada tali itu dengan kecepatan 5 m/s. Titik P berada pada jarak 2,25 m. Pada saat sumber getar telah bergetar 1,5 sekon dan arah gerak pertama kalinya ke atas, tentukan kecepatan dan percepatan di titik P!

Jawaban:

begin mathsize 14px style lambda equals v over f equals 5 over 5 equals 1 space straight m  v subscript p equals omega space A space cos space open parentheses omega t minus k x close parentheses space space space space equals 2 pi open parentheses 5 close parentheses cross times 8 cross times 10 to the power of negative 2 end exponent space cos space 2 pi open parentheses f open parentheses t close parentheses minus x over lambda close parentheses space space space space equals 0 comma 8 pi space cos space space 2 pi open parentheses open parentheses 5 cross times 1 comma 5 close parentheses minus fraction numerator 2 comma 25 over denominator 1 end fraction close parentheses space space space space equals 0 comma 8 pi space cos space space 2 pi open parentheses 5 comma 25 close parentheses space space space space equals 0 comma 8 pi space cos space space 10 comma 5 pi space space space space equals 0 comma 8 pi space open parentheses 0 close parentheses space space space space equals 0  a subscript p equals negative w squared space y subscript p space space space space equals negative w squared space open parentheses A space sin space left parenthesis omega t minus k x right parenthesis close parentheses space space space space equals negative open parentheses 2 pi f close parentheses squared space open parentheses A space sin space left parenthesis omega t minus k x right parenthesis close parentheses space space space space equals negative open parentheses 2 pi open parentheses 5 close parentheses close parentheses squared space open parentheses 8 cross times 10 to the power of negative 2 space end exponent sin space 2 pi left parenthesis f open parentheses t close parentheses minus x over lambda right parenthesis close parentheses space space space space equals negative 100 pi squared space space open parentheses 8 cross times 10 to the power of negative 2 space end exponent sin space 2 pi left parenthesis open parentheses 5 cross times 1 comma 5 close parentheses minus fraction numerator 2 comma 25 over denominator 1 end fraction right parenthesis close parentheses space space space space equals negative 100 pi squared space space open parentheses 8 cross times 10 to the power of negative 2 space end exponent sin space 10 comma 5 pi close parentheses space space space space equals negative 100 pi squared space space open parentheses 8 cross times 10 to the power of negative 2 space end exponent cross times 1 close parentheses space space space space equals negative 8 pi squared end style  

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