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\begin{document}

\frame{\frametitle{\b Oscillations - 1} \bigskip

{\bf Spring Constant (1):} $\kappa=m\,\omega^2$.
\bigskip

{\bf Spring Block Oscillation (2):} Take derivatives of
$$ x = x_{\max}\,\sin(\omega\,t)\,, $$
and use $\max[\sin(\omega\,t)]=1$.
\bigskip

{\bf Mass on Spring (3).} New equilibrium position: $M\,g=k\,x_0$ 
with 

$x_0$ amplitude. Lowest point in oscillation seen from starting 
point: $x_{\min}=2\,x_0$. Frequency: $f=\omega/(2\pi)$ in units
$1/s$ or $Hz$. Note: angular frequency $\omega$ in $rad$ is not 
accepted.
\bigskip

{\bf Mass, Spring on Air Track (4):} 
$$x=x_{\max}\,\cos(\omega\,t)~~{\rm with}~~x_{\max}~~{\rm and}~~T$$ 
given. 
\vskip 20pt }


\frame{\frametitle{\b Oscillations - 2} \bigskip

{\bf Spring Force (5):} \vskip -20pt
$$ k=\frac{M_2\,g}{\triangle x}~~~
   {\rm and}~~\omega = \sqrt\frac{k}{M_1}\,.$$
\medskip

{\bf Spring Height Motion (6):} 
$$ x = \frac{M\,g}{k}\,.$$
\medskip

{\bf Block and Spring (7).} The contact time is half (!) a period
$$ t=\frac{\pi}{\omega}\,,~~\omega=?\,.~~~~{\rm Then}~~
   \triangle x = v_0\,\omega\,.$$


\vskip 20pt }

\end{document}
