Persamaan simpangan suatu partikel yang bergetar harmonik adalah y = 18 sin 40 π t, y dalam centimeter dan t dalam sekon. Frekuensi simpangan partikel adalah….

Persamaan simpangan suatu partikel yang bergetar harmonik adalah y = 18 sin 40 π t, y dalam centimeter dan t dalam sekon. Frekuensi simpangan partikel adalah….

Jawaban yang benar adalah 20 Hz.

Diketahui:
y = 18 sin 40πt cm ⇒ ω = 40π rad/s

Ditanya: f = .. ?

Pembahasan:

Gerak harmonik adalah suatu gerak bolak-balik melalui titik keseimbangan. Secara umum, simpangan pada gerak harmonik dirumuskan:

y = A sin ωt

Keterangan:
y : simpangan (m)
A : amplitudo (m)
ω : frekuensi sudut (rad/s)
t : waktu (s)

Frekuensi didefinisikan sebagai jumlah getaran tiap satuan waktu. Hubungan antara frekuensi dan frekuensi sudut dirumuskan:

ω = 2πf

Keterangan:
ω : frekuensi sudut (rad/s)
f : frekuensi (Hz)
π : 3,14 atau 22/7

Maka diperoleh:

ω = 2πf
40π = 2π x f
f = 40π / 2π
f = 20 Hz

Jadi, frekuensi simpangan partikel adalah 20 Hz.

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