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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 g Ö+sin(0) = 0, + 1/ s L The pendulum oscillation is described by the initial-value problem consisting of the equation of motion with initial conditions: 0 (to) = 0o,0 (to) = wo Here, L is the length of the pendulum, g acceleration due to gravity, the angle the pendulum makes with the vertical, 00 the initial angular displacement, and to the initial angular velocity. a) Transform the second-order initial-value problem into a system of first-order initial-value problems. П 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. = 4

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 g Ö+sin(0) = 0, + 1/ s L The pendulum oscillation is described by the initial-value problem consisting of the equation of motion with initial conditions: 0 (to) = 0o,0 (to) = wo Here, L is the length of the pendulum, g acceleration due to gravity, the angle the pendulum makes with the vertical, 00 the initial angular displacement, and to the initial angular velocity. a) Transform the second-order initial-value problem into a system of first-order initial-value problems. П 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. = 4

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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 g Ö+sin(0) = 0, + 1/ s L The pendulum oscillation is described by the initial-value problem consisting of the equation of motion with initial conditions: 0 (to) = 0o,0 (to) = wo Here, L is the length of the pendulum, g acceleration due to gravity, the angle the pendulum makes with the vertical, 00 the initial angular displacement, and to 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. 4
Transcribed Image Text: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 g Ö+sin(0) = 0, + 1/ s L The pendulum oscillation is described by the initial-value problem consisting of the equation of motion with initial conditions: 0 (to) = 0o,0 (to) = wo Here, L is the length of the pendulum, g acceleration due to gravity, the angle the pendulum makes with the vertical, 00 the initial angular displacement, and to 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. 4
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