### Simple Pendulum and Simple Harmonic MotionA simple pendulum with a length of 2.23 meters and a mass of 6.74 kg is given an initial speed of 2.06 meters per second (m/s) at its equilibrium position. The pendulum undergoes simple harmonic motion. #### Problems to Solve:1. **Period (T)**: - The time taken for one complete cycle of the pendulum's swing.2. **Total Energy (E)**: - The sum of the kinetic and potential energy in the system.3. **Maximum Angular Displacement (θ_max)**: - The furthest angle from the equilibrium position the pendulum reaches.4. **Equation for Angular Position as a Function of Time**: - This expresses the pendulum's angular displacement over time.#### Solutions:- **Period (T)**: \( T = 3.00 \, \text{s} \) - **Total Energy (E)**: \( E = 14.3 \, \text{J} \) - **Maximum Angular Displacement (θ_max)**: \( \theta_{\text{max}} = 0.441 \, \text{rad} \) - **Equation for Angular Position (θ)**: \[ \theta(t) = 0.441 \, \text{rad} \sin(2.10 \, \text{s}^{-1} t) \]The equation above shows that the pendulum's angular position oscillates as a sine function, where:- \( 0.441 \, \text{rad} \) is the amplitude,- \( 2.10 \, \text{s}^{-1} \) is the angular frequency,- \( t \) is the time variable.### Explanation of Key Terms:- **Simple Harmonic Motion**: - This is the type of oscillation where the restoring force is directly proportional to the displacement and acts in the direction opposite to that displacement.- **Angular Displacement (θ)**: - The angle through which the pendulum has swung from its equilibrium (rest) position.- **Amplitude**: - The maximum displacement from the equilibrium position in simple harmonic motion.- **Angular Frequency (ω)**: - Related to the period, it describes how many oscillations occur in a unit of time.This model assumes

Name: ### Simple Pendulum and Simple Harmonic MotionA simple pendulum with
Uploaded: 2024-03-20T06:58:04.000Z
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Description: ### Simple Pendulum and Simple Harmonic MotionA simple pendulum with a length of 2.23 meters and a mass of 6.74 kg is given an initial speed of 2.06 meters per second (m/s) at its equilibrium position. The pendulum undergoes simple harmonic motion.