If the differential equation for a simple harmonic motion is (d2y/dt2)+2y=0, the time-period of the motion is

Question

If the differential equation for a simple harmonic motion is (d2y/dt2)+2y=0, the time-period of the motion is (A) π√2 sec (B) (√2s/π) sec (C) (π/√2) sec (D) 2π sec

Tardigrade Admin · Accepted Answer

The differential equation of simple harmonic motion is

\frac{d ^{2} y}{d t ^{2}} + 2 y = 0

or

\frac{d ^{2} y}{d t ^{2}} = - 2 y ... (i)

Standard equation of simple harmonic motion is

\frac{d ^{2} y}{d t ^{2}} = - ω^{2} y ... (ii)

Comparing eq.

(i)

and

(ii)

,

ω^{2} = 2

or

ω = 2

As we know,

ω = \frac{2 π}{T}

∴

Time period,

T = \frac{2 π}{ω} = \frac{2 π}{2} = π 2 sec

Q. If the differential equation for a simple harmonic motion is $\frac{d ^{2} y}{d t ^{2}} + 2 y = 0,$ the time-period of the motion is

$π 2$ sec

$\frac{2 s}{π}$ sec

$\frac{π}{2}$ sec

$2 π$ sec

Q. If the differential equation for a simple harmonic motion is dt2d2y​+2y=0, the time-period of the motion is

π2​ sec

π2​s​ sec

2​π​ sec

2π sec

The differential equation of simple harmonic motion is dt2d2y​+2y=0 or dt2d2y​=−2y...(i) Standard equation of simple harmonic motion is dt2d2y​=−ω2y...(ii) Comparing eq. (i) and (ii), ω2=2 or ω=2​ As we know, ω=T2π​ ∴ Time period, T=ω2π​=2​2π​=π2​sec

Q. If the differential equation for a simple harmonic motion is $\frac{d ^{2} y}{d t ^{2}} + 2 y = 0,$ the time-period of the motion is

$π 2$ sec

$\frac{2 s}{π}$ sec

$\frac{π}{2}$ sec

$2 π$ sec