4. [10 Pts] A harmonic excitation (above wo) at 102 Rad/s causes a beating at 1 Rad/s in undamped torsional oscillator with mass M = 1 kg, radius R = 0.5 m, and thickness h = 0.2 m. F(t) M 2R Massless Shaft (a) What is the natural frequency in Rad/s and Hz? [2 Pt] (b) What is the torsional spring constant of the shaft? (Idisk=MR/2) [1 Pt] (c) The entire disk is now submerged in water. Let's say the damping force is proportional to the submerged side area of the disk. What is the areal damping coefficient (y/area) if the free vibration of this system is critically damped? [3 Pts] (d) The disk is now only half submerged in water. What is the amplification ratio? Ignore water splash from drag. [3 Pts] (e) Continuing from (d), what is the quality factor? [1 Pt]