Problem 3. In Introductory Mechanics, you learned about simple harmonic oscillators. One such system is known as a torsion pendulum, shown below. Here the element of "springiness" is associated with the twisting of the suspension wire rather than the extension or compression of a spring ("torsion" refers to this twisting). Rotating the disk in either direction by an angle 8 introduces a "restoring" torque of T = -K0, where K is the torsion constant specific to the suspension wire, the way the spring constant k is for a spring, Derive the equation of motion for a torsion pendulum as well as the equation for the period (T) of its oscillation.

Problem 3. In Introductory Mechanics, you learned about simple harmonic oscillators. One such system is known as a torsion pendulum, shown below. Here the element of "springiness" is associated with the twisting of the suspension wire rather than the extension or compression of a spring ("torsion" refers to this twisting). Rotating the disk in either direction by an angle 8 introduces a "restoring" torque of T = -K0, where K is the torsion constant specific to the suspension wire, the way the spring constant k is for a spring, Derive the equation of motion for a torsion pendulum as well as the equation for the period (T) of its oscillation.