If a simple harmonic motion is represented by $\frac{d^{2} x}{d t^{2}} + α x = 0$ , its time period is then
$2 π \sqrt{α}$ .
$2 π α$
$\frac{2 π}{\sqrt{α}}$
$\frac{2 π}{α}$

Question

If a simple harmonic motion is represented by dfrac-d-2 x-d t-2- - alpha x - 0- its time period is then2 pi sqrt-alpha-2 pi alphadfrac-2 pi-sqrt-alpha-dfrac-2 pi-alpha-

Toppr Admin · Accepted Answer

The equation of SHM-xA0-d2xdt2-x3B1-x-0 or d2xdt2-x2212-x3B1-xComparing it with the equation of SHMd2xdt2-x2212-x3C9-2x-x3C9-2-x3B1-or-x3C9-x221A-x3B1-x2234-T-2-x3C0-x3C9-2-x3C0-x221A-x3B1-

If a simple harmonic motion is represented by d2xdt2+αx=0, its time period is then2π√α.2πα2π√α2πα

The equation of SHM, d2xdt2+αx=0 or d2xdt2=−αxComparing it with the equation of SHMd2xdt2=−ω2x;ω2=αorω=√α∴T=2πω=2π√α.

If a simple harmonic motion is represented by $\frac{d^{2} x}{d t^{2}} + α x = 0$ , its time period is then
$2 π \sqrt{α}$ .
$2 π α$
$\frac{2 π}{\sqrt{α}}$
$\frac{2 π}{α}$

The equation of SHM,
$\frac{d^{2} x}{d t^{2}} + α x = 0$ or $\frac{d^{2} x}{d t^{2}} = - α x$
Comparing it with the equation of SHM
$\frac{d^{2} x}{d t^{2}} = - ω^{2} x; ω^{2} = α o r ω = \sqrt{α} ∴ T = \frac{2 π}{ω} = \frac{2 π}{\sqrt{α}}$ .