Question

Figure shows a torisional pendulum consists of a uniform disc D of mass M and radius R attached to a this rod of torisional constant C. Find the amplitude and the energy of small torisional oscillations of the disc, if initially the disc was imparted angular speed ω₀ .

Answer 1

We know for a torisional pendulum angular frequency of small oscillations is given as

Where I = 1/2MR² , thus

At it is given that from mean position the disc is imparted as\an angular speed ω₀ , if the angular amplitude of oscillations of disc is β, we have

Thus angular amplitude is given as

For angular SHM the total oscillation energy is given as

Thus here oscillation energy of the disc is given as