Answer to Question #336461 in Quantum Mechanics for Fedii

Question #336461

Show that simple harmonic motion y(t) = C1 cos ωt + C2 sin ωt can be written as:


a. y(t) = A sin(ωt + ϕ0)


b. y(t) = A cos(ωt + ϕ1)


1
Expert's answer
2022-05-02T18:06:11-0400

"A=\\sqrt{C_1^2+C_2^2},"

"\\phi_0=\\arccos\\frac{C_2}{\\sqrt{C_1^2+C_2^2}},"

"\\phi_1=-\\arcsin\\frac{C_2}{\\sqrt{C_1^2+C_2^2}}."


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