Question

If a simple harmonic motion is represented by

d2x/dt2 +αx =0 , its time period is then ____

A)2π/√a
B)2π/√3
C)2π/√x
D)2π/a

Answer 1

The time period of the simple harmonic motion represented by the given equation d²x/dt² + αx = 0 is 2π/√α.

Step-by-step explanation:

The given equation, d²x/dt² + αx = 0, represents a simple harmonic motion. The time period of a simple harmonic motion can be determined using the equation T = 2π/ω, where ω is the angular frequency given by ω = √α.

Comparing the given equation with the equation of motion for simple harmonic motion (d²x/dt² + ω²x = 0), we can see that α is equivalent to ω². Therefore, the time period of the simple harmonic motion represented by the given equation is T = 2π/√α.

Therefore, the correct answer is A) 2π/√α.