A simple pendulum is idealized by considering a bob mass swinging on an inextensible, massless rod...

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A simple pendulum is idealized by considering a bob mass swinging on an inextensible, massless rod (negligible mass relative to the bob) about a frictionless pivot (Figure 1). 0 L Figure 1 Simple pendulum The pendulum oscillation is described by the initial-value problem consisting of the equation of motion with initial conditions: 0+ sin(0) = 0, 0(to) = 0o,8(to) = wo Here, L is the length of the pendulum, g acceleration due to gravity, the angle the pendulum makes with the vertical, 0, the initial angular displacement, and coo the initial angular velocity. a) Transform the second-order initial-value problem into a system of first-order initial-value problems. b) Compute the angular displacement 0 (0.2) and angular velocity (0.2) using the forward Euler method with step size h = 0.1. Use L = 0.5 m, g = 9.81 m/s², to= 0, 0o = rad, and wo = 0 rad/s. A simple pendulum is idealized by considering a bob mass swinging on an inextensible, massless rod (negligible mass relative to the bob) about a frictionless pivot (Figure 1). 0 L Figure 1 Simple pendulum The pendulum oscillation is described by the initial-value problem consisting of the equation of motion with initial conditions: 0+ sin(0) = 0, 0(to) = 0o,8(to) = wo Here, L is the length of the pendulum, g acceleration due to gravity, the angle the pendulum makes with the vertical, 0, the initial angular displacement, and coo the initial angular velocity. a) Transform the second-order initial-value problem into a system of first-order initial-value problems. b) Compute the angular displacement 0 (0.2) and angular velocity (0.2) using the forward Euler method with step size h = 0.1. Use L = 0.5 m, g = 9.81 m/s², to= 0, 0o = rad, and wo = 0 rad/s.

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Step 1 Solution of a given 6 sinQ 0 Initial Condition 0t 0 ... View the full answer