A grandfather clock uses a pendulum to measure time. A model of this pendulum is constructed as follows: One end of a rod of length { = 1.0 m and mass mrod = 0.65 kg is connected to a bearing (assume friction-less) and the other end connects to a solid cylinder of radius R= 0.12 m. You wish to find the mass of the cylinder such that the period of oscillation is T = 2 s. 1. Find the moment of inertia of the rod and disk. 2. Calculate the distance between the pivot and the center of mass of the pendulum. 3. Calculate the mass of the cylinder such that the period of oscillation is T = 2s. 4. Write down the equation of motion of the cylinder 0(t), assuming the angle of release is small sin(0) = 0). 5. Determine the velocity of the pendulum bob after swinging for 0.73 s, if the pendulum is released from a maximum release angle of 0 = 0.1 rad at time t = 0.
A grandfather clock uses a pendulum to measure time. A model of this pendulum is constructed as follows: One end of a rod of length { = 1.0 m and mass mrod = 0.65 kg is connected to a bearing (assume friction-less) and the other end connects to a solid cylinder of radius R= 0.12 m. You wish to find the mass of the cylinder such that the period of oscillation is T = 2 s. 1. Find the moment of inertia of the rod and disk. 2. Calculate the distance between the pivot and the center of mass of the pendulum. 3. Calculate the mass of the cylinder such that the period of oscillation is T = 2s. 4. Write down the equation of motion of the cylinder 0(t), assuming the angle of release is small sin(0) = 0). 5. Determine the velocity of the pendulum bob after swinging for 0.73 s, if the pendulum is released from a maximum release angle of 0 = 0.1 rad at time t = 0.
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Transcribed Image Text:A grandfather clock uses a pendulum to measure time. A model of this pendulum is constructed as follows: One
end of a rod of length l = 1.0 m and mass m,od = 0.65 kg is connected to a bearing (assume friction-less) and the
other end connects to a solid cylinder of radius R = 0.12 m. You wish to find the mass of the cylinder such that the
period of oscillation is T = 2 s.
1. Find the moment of inertia of the rod and disk.
2. Calculate the distance between the pivot and the center of mass of the pendulum.
3. Calculate the mass of the cylinder such that the period of oscillation is T = 2s.
4. Write down the equation of motion of the cylinder 0(t), assuming the angle of release is small sin(0) = 0).
5. Determine the velocity of the pendulum bob after swinging for 0.73 s, if the pendulum is released from a
maximum release angle of 0 = 0.1 rad at time t = 0.
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