PHYSICS - physical pendulum - Need your help

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SUMMARY

The discussion focuses on the analysis of a physical pendulum consisting of a uniform rod with a length of 1.5 meters and a mass of 5 kg, pivoted at one end. Key calculations include determining the period of oscillation, the angular displacement function θ(t), the angular kinetic energy after 1 second, and the maximum torque during oscillation. The initial conditions include an angle of θ0 = 0.2 rad and an instantaneous angular velocity of -0.5 rad/sec. Participants emphasize the importance of showing work for clarity and to facilitate assistance.

PREREQUISITES
  • Understanding of physical pendulum dynamics
  • Knowledge of angular displacement and velocity
  • Familiarity with energy conservation principles in rotational motion
  • Basic proficiency in solving differential equations related to oscillatory motion
NEXT STEPS
  • Calculate the period of a physical pendulum using the formula T = 2π√(I/mgh)
  • Derive the angular displacement function θ(t) for a simple harmonic oscillator
  • Evaluate angular kinetic energy using the formula KE = 0.5 * I * ω²
  • Determine maximum torque using τ = r × F and analyze forces acting on the pendulum
USEFUL FOR

Physics students, educators, and anyone interested in understanding the dynamics of oscillatory systems, particularly those involving physical pendulums.

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A physical pendulum consists of a uniform rod of length L = 1.5 meters. The mass of the rod is 5kg and the rod is pivoted about its end. The rod is pulled out to an angle of θ0=0.2rad and is then given a push so that its instantaneous angular velocity is -0.5 rad/sec.
a) What is the period of the oscillator?
b) Determine the function for θ(t), the angular displacement from vertical as a function of time.
c) What is the angular kinetic energy of the rod after 1.0 sec?
d) What is the maximum torque on the rod during the course of its oscillation?
 
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Will you show your works so that it might be easy to help. The basic thing to start with is initial kinetic energy and then use energy conservatin to relate it to find other things. Specific helps will be given only after you show that you tried it.
 

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