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A simple harmonic oscillator has a mass M0 on a spring of force constant k. The system is damped. It takes 10 cycles for the amplitude of the oscillations to decay to 37% of the original value (i.e. 1/e).

a) If I double the mass to 2M0 how many cycles will it take to decay to 1/e? (assume b in F(damping)=(-b*v), stays the same.) (Hint: Look at what happens to 'beta' and omega when you change the mass.)

b). I change the mass, but leave the damping force, (-b*v), the same, i.e. b is the same for both masses. If it is now critically damped, what is the new mass M1 in terms of M0?

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