\magnification=\magstep1

$$
y(t) \quad = \quad y_{\rm max} \cos ( \omega t + \phi )
$$

$$
v_{y}(t) \quad = \quad {{ dy}\over{dt}} \quad = 
            \quad -\omega y_{\rm max} \sin ( \omega t + \phi )
$$

$$
{\rm KE_{max}} \quad = \quad {{1}\over{2}} m v_{\rm max}^2 
$$

$$
{\rm Energy } \quad = \quad {{1}\over{2}} m v_{\rm max}^2 
$$

$$
{\rm Energy } \quad = \quad {{1}\over{2}} m \thinspace \omega^2 y_{\rm max}^2 
$$

$$
{\rm Energy } \quad = \quad {{1}\over{2}} \left( \mu v T \right)  \thinspace \omega^2 y_{\rm max}^2 
$$

$$
{\rm Power } \quad = \quad { {\rm Energy}\over{\rm Time} } \quad = 
       \quad {{1}\over{2}} \left( \mu v \right)  \thinspace \omega^2 y_{\rm max}^2 
$$

$$
v \quad = \quad { {\omega} \over {k} }
$$

$$
{\rm Power } \quad =  \quad {{1}\over{2}}  { {\mu} \over {k} }   \thinspace \omega^3 y_{\rm max}^2 
$$




\bye 
