5 A \(\mathbf { p }\) rticle \(P \mathbf { 6 }\) mass \(m\) is attach d to e. a lig in k en ib e strig leg h \(a\). Tb o b re. th strig s attach d or fiæ \(\Phi \quad n O\).
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Th \(\boldsymbol { p }\) rticle \(P\) mo sinab izo al circle with a co tan ag arsp ed \(\omega\) with th strig in lie d at \(\theta\) to \(\mathrm { b } \quad \mathrm { m }\) ard rtical th \(\mathrm { g } \quad O\) (see \(\dot { \mathrm { d } } \mathrm { ag } \mathrm { am }\) ).
Sw that \(\omega ^ { 2 } = \frac { 2 g } { a }\).- Th \(\mathbf { p }\) rticle w has at restad stan e \(a\) rtically b low \(O\). It isth \(\mathrm { np } \dot { \mathrm { p } }\) ected b izb ally so th t it \(\mathbf { b } \mathbf { g }\) s to m in a rtical circle with cen re \(O\). Wh n th strig maks an ag e \(\boldsymbol { \theta }\), with th d \(\mathbb { w }\) ard rtical th \(\mathbf { g } O\), th ang arse \(\operatorname { d } P\) is \(\sqrt { \frac { 2 g } { a } }\). Tb strig first \(\mathbf { g }\) s slack when \(O P\) mak s ara g e \(\theta\) with b ard rtical th ob \(O\).
Fid b le 6 co \(\theta\).