Answer:12.34 rad/s
Explanation:
We know in torsional pendulum
[tex]I\ddot{\theta }=-k\theta [/tex]
[tex]\ddot{\theta }+\omega ^2\theta =0[/tex]
[tex]\omega ^2=\frac{k}{I}[/tex]
general equation of it
[tex]\theta \left ( t\right )=\theta _0cos\omega t[/tex]
and at t=0 \theta =45[/tex]
[tex]\frac{\pi }{4}=\theta _0[/tex]
[tex]\theta \left ( t\right )=\frac{\pi }{4}cos\omega t[/tex]
and [tex]\omega =2\pi f=5\pi [/tex]
For angular velocity
[tex]\frac{\mathrm{d}\theta }{\mathrm{d}t}=-\frac{5\pi ^2}{4}sin5\pi t[/tex]
Maximum angular velocity=[tex]\frac{5\pi ^2}{4}=12.34 rad/s[/tex]
