If a simple harmonic motion is represented by d2xdt2 + αx = 0, its time period is:
Question
If a simple harmonic motion is represented by
d²x/dt² + αx = 0, its time period is:
Solution
The equation you provided is the differential equation for simple harmonic motion (SHM). In this equation, α is the angular frequency squared (ω²).
The general form of the equation for SHM is d²x/dt² + ω²x = 0.
The angular frequency ω is related to the period of the motion T by the equation ω = 2π/T.
Therefore, you can solve for T by rearranging this equation to get T = 2π/ω.
Since ω² = α, you can take the square root of α to find ω.
So, the period T of the simple harmonic motion is given by T = 2π/√α.
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