A small mass, m = 50.0 g, is attached to the end of a massless rod that is hanging from the ceiling and is free to swing. The rod has length L = 1.00 m. The rod is displaced 10.0° from the vertical and released at time t = 0. Neglect air resistance. What is the period of the rod’s oscillation? Now suppose the entire system is immersed in a fluid with a small damping constant, b = 0.0100 kg/s, and the rod is again released from an initial displacement angle of 10.0°. What is the time for the amplitude of the oscillation to reduce to 5.00°? Assume that the damping is small. Also note that since the amplitude of the oscillation is small and all the mass of the pendulum is at the end of the rod, the motion of the mass can be treated as strictly linear, and you can use the substitution Rθ (t) = x(t), where R =1.0 m is the length of the pendulum rod.
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