\magnification=\magstep2


$$
  \vec{F} \quad = \quad -k \thinspace \vec{x} 
$$


$$
  \vec{F} \quad = \quad m \vec{a} \quad = \quad m { {d^2 {\vec{x}}}\over{dt^2} }
$$

$$
  m { {d^2 {\vec{x}}}\over{dt^2} } \quad = \quad - k \vec{x} 
$$
  
$$
  { {d^2 {\vec{x}}}\over{dt^2} } \quad = \quad - \left ( {{k}\over{m}} \right )  \thinspace \vec{x}  
$$

$$
  { {d^2 {\vec{x}}}\over{dt^2} } \quad = \quad - {\omega}^2  \thinspace \vec{x}  
$$

$$
  x(t) \quad = \quad A \cos \left( 
           \sqrt{{{k}\over{m}}} t \thinspace + \thinspace \phi
            \right)
$$

$$
  \omega \quad = \quad \sqrt{ {k}\over{m} }
$$

$$
  x(t) \quad = \quad A \cos \left( 
           \omega t \thinspace + \thinspace \phi
            \right)
$$
\bye
