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.

Question

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.

Knowee AI · Accepted Answer

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.

If a simple harmonic motion is represented by d2xdt2 + αx  =  0, its time period is: