Oscillatory motion

Oscillatory Motion

• Units and Variables

  • ω - angular frequency, in radians per second
  • A - amplitude, in meters
  • φ - phase contant, in radians
  • f -frequency, in Hertz
  • T - period, seconds per cycle
• $x\left(t\right)=A\cos \left(\omega t+\phi \right)$
• $v\left(t\right)=-\omega A\sin \left(\omega t+\phi \right)$
• $a\left(t\right)=-{\omega }^{2}A\cos \left(\omega t+\phi \right)$
• $\omega =2\pi f=\sqrt{\frac{k}{m}}$
• $f=\frac{1}{T}=\frac{\omega }{2\pi }$
• $T=\frac{1}{f}=\frac{2\pi }{\omega }$
• $v=\pm \omega \sqrt{A^2-x^2}$
• $v_{\text{max}}=\omega A=\sqrt{\frac{k}{m}}A$
• $a_{\text{max}}={\omega }^{2}A=\frac{k}{m}A$

• Pendulum

  • $\omega =\sqrt{\frac{g}{L}}$

• Physical Pendulum

  • $\omega =\sqrt{\frac{mgd}{I}}$