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Harmon Keeling

Feb 20, 2025

Harmonic Oscillator Equation question!?

At what time t1 does the block come back to its original equilibrium position (x=0) for the first time?Express your answer in terms of some or all of the variables: A, k, and m. I tried working out the problem myself but I came up with the wrong answer! My answer: (arccos 0^2 x m) / k
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The differential equation for a harmonic oscillator ism d²x(t)/dt² = -kxwith the general solutionx(t) = A*cos(ωt +φ)ω = √(k/m)φ can be derived from initial condition. I think for this problem the oscillator started its motion at x=A, hence φ=0 x(t1) = A*cos(ωt1) = 0orcos(ωt1) = 0The cosine is zero for ωt1 = 1/2 π , 3/2 π, 5/2 π;7/2 π,…hencet1 = π / (2ω) = π/2 * √(m/k)... Show More
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For the best answers, search on this site https://shorturl.im/zwRmdSorry, you seem to have missed out the equation, and probably some earlier parts of the question. try again?... Show More
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