Consider a massless pendulum of length L and a bob of mass m at its end moving through oil. The massive bob undergoes small oscillations, but the oil regards the bob’s motion with a resistive force proportional to the speed with Fd=-b*θ. The bob is initially pulled back at t=0 with θ = αlpha with zero velocity. (a) Write down the differential equation governing the motion of the pendulum. (b) Find the angular displacement as a function of time by solving (a). Assume that b is smaller than the natural frequency (frequency in the absence of damping) of the pendulum. (c) Find the mechanical energy of the pendulum as a function of time. (d) Find the time when the mechanical energy decays to 1/e of its initial value.
Consider a massless pendulum of length L and a bob of mass m at its end moving through oil. The massive bob undergoes small oscillations, but the oil regards the bob’s motion with a resistive force proportional to the speed with Fd=-b*θ. The bob is initially pulled back at t=0 with θ = αlpha with zero velocity. (a) Write down the differential equation governing the motion of the pendulum. (b) Find the
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