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: 8 += sin(0) = 0, e(to) = 0o, (to) = wo Here, L is the length of the pendulum, g acceleration due to gravity, the angle the pendulum makes with the vertical, 90 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 (0.2) 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, 00=rad, and wo = 0 rad/s.

A force of 15 Newtons stretches a spring 20 centimeters. After a 3 kilogram mass is attached to the spring, the mass is pulled down to a position √3 meters below equilibrium and released with an upward velocity of 5 meters per second. Find a. The equation of motion. b. The amplitude, period, and phase shift of the simple harmonic motion.

please answer part c only. there are no external forces. and show work