Mathematics, Differential Equations, Calculus, Physics, Classical Mechanics.
cos(x) and sin(-x) = -sin(x) as cosine is an even function and sine is an odd function. Now if we let t = 0, we get x(0) = c₃ meaning that c₃ is just the initial position, x₀. Additionally, if we differentiate x(t) and let t = 0 again we get x’(0) = ωc₄, or in other words c₄ = v₀/ω where v₀ is the