3. Sebuah partikel melakukan gerak harmonis sederhana dengan persamaan simpangan y = 5 sin (4лt + 0,25n). Satuan y dalam cm dan t dalam sekon. Simpangan, kecepatan, dan percepatan saat t = 4 s adalah....
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Jawaban:
Penjelasan:
Simpangan = y, Kecepatan = y' = v, Percepatan = y'' = v' = a
[tex]y(4) = 5\sin(4\pi \cdot 4 + 0.25\pi)\\\\y(4) = 5\sin(16\pi+0.25\pi)\\\\\Large{\boxed{\boxed{\boldsymbol{y(4) = 5\sin(0.25\pi) = \dfrac{5}{2}\sqrt{2} \; \text{m} \approx 3.5355 \; \text{m}}}}}\\\\\\v(4) = 5\cdot 4\pi \cdot \cos(16\pi+0.25\pi)\\\\v(4) = 20\pi \cdot \cos(0.25\pi)\\\\\Large{\boxed{\boxed{\boldsymbol{v(4) = 10\sqrt{2}\pi \approx 44.43 \;\dfrac{\text{m}}{\text{s}}}}}}\\\\\\a(4) = -20\pi \cdot 4\pi \cdot \sin(16\pi+0.25\pi)\\\\a(4) = -80\pi^2 \cdot \sin(0.25\pi)\\\\[/tex]
[tex]\huge{\boxed{\boxed{\boldsymbol{a(4) = -40\sqrt{2}\pi^2\;\dfrac{\text{m\[^2\]}}{\text{s}}\approx -469.48 \;\dfrac{\text{m\[^2\]}}{\text{s}}}}}[/tex]
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