=for timestamp
So Jun 26 12:20:23 CEST 2005

=head3 51. Hausaufgabe

=head4 Blatt

=for comment
Schon vor paar Tagen, Do, den 23.6.2005, glaub' ich.

M<l = 1,\!09\mathrm{m}; \alpha_{\mathrm{max}} = 4,\!0^\circ;>

=over

=item a)

M<T = 2\pi \sqrt{\dfrac{l}{g}} = \ldots = 2,\!1\mathrm{s};>

M<A = l \alpha_{\mathrm{max}} = \ldots = 7,\!6\mathrm{cm};>

=item b)

M<v_{\mathrm{max}} = A \omega = A \dfrac{2\pi}{T} =
0,\!23\frac{\mathrm{m}}{\mathrm{s}};>

=item c)

M<\alpha = 2,\!0^\circ;>

M<y = l \alpha = A \cdot \sin \omega{}t = l \alpha_{\mathrm{max}}
\sin\!\left[\dfrac{2\pi}{T} t\right]; \Rightarrow
\dfrac{\alpha}{\alpha_{\mathrm{max}}} = \sin\!\left[\dfrac{2\pi}{T} t\right];>

⇒ M<\arcsin\!\left[\dfrac{\alpha}{\alpha_{\mathrm{max}}}\right] =
\dfrac{2\pi}{T} t; \Rightarrow t = \dfrac{T}{2\pi}
\arcsin\!\left[\dfrac{\alpha}{\alpha_{\mathrm{max}}}\right] = \ldots =
0,\!18\mathrm{s};>

=item d)

M<v(t) = A\omega \cdot \cos \omega{}t;>

M<v(0,\!18\mathrm{s}) = \ldots = 0,\!20\frac{\mathrm{m}}{\mathrm{s}};>

=back