6. A damped mechanical harmonic oscillator is driven by a sinusoidal force Fosinmt) at frequency to. The nearby figure shows the oscillator resonance curve or the mean power input as a function of drive frequency with peak value Pm. The mean power falls to Mean input power fol _. "U 5 Pm/Z at frequencies 0. 96w0 and 1. 04%, so the system is deep in the underdamped limit. 0 L/ ,_i_l_.e__.w 0.96030 (no 1.04miJ a. Find the quality factor Q for the oscillator. b. If the driving force is removed, the energy of the oscillator decays exponentially: 130:) = E037\". What is the value of the decay constant y? c. If the driving force is removed, what fraction of the energy is lost per full cycle? A new system is made with the spring constant doubled, but the mass and the damping force are unchanged. The same driving force Fusinaut) is applied to the new system. d. What is the new resonance frequency 030' in terms of the original frequency 030? . What is the new quality factor Q' in terms of the original Q ? f. What is the new maximum mean power input Pm' in terms of the original Pm ? 9. What is the new total energy 130' of the system at resonance in terms of the original EU