If the differential equation for a simple harmonic motion is (d2 y/dt2) + 2 y = 0, the time-period of the motion is

Question

If the differential equation for a simple harmonic motion is (d2 y/dt2) + 2 y = 0, the time-period of the motion is (A) π √2 s  (B)  (√2/π) s  (C)  (π/√2) s  (D) 2 π s

Tardigrade Admin · Accepted Answer

Given, (d2 y/d t2)+2 y=0 ...(i) But, we know that (d2 y/d t2)+ω2 Y=0 ...(ii) Comparing both equation, we get ω2 =2 ⇒ ω =√2 The periodic time T=(2 π/ω)=(2 π/√2) =√2 π=π √2 s

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

$π 2 s$

$\frac{2}{π} s$

$\frac{π}{2} s$

$2 π s$

$\frac{π}{2} s$

Given,
$\frac{d ^{2} y}{d t ^{2}} + 2 y = 0 ... (i)$
But, we know that
$\frac{d ^{2} y}{d t ^{2}} + ω^{2} Y = 0 ... (ii)$
Comparing both equation, we get
$ω^{2} = 2$
$\Rightarrow ω = 2$
The periodic time
$T = \frac{2 π}{ω} = \frac{2 π}{2}$
$= 2 π = π 2 s$

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

π2​s

π2​​s

2​π​s

2πs

2π​​s

Given, dt2d2y​+2y=0...(i) But, we know that dt2d2y​+ω2Y=0...(ii) Comparing both equation, we get ω2=2 ⇒ω=2​ The periodic time T=ω2π​=2​2π​ =2​π=π2​s

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

$π 2 s$

$\frac{2}{π} s$

$\frac{π}{2} s$

$2 π s$

$\frac{π}{2} s$

Given,
$\frac{d ^{2} y}{d t ^{2}} + 2 y = 0 ... (i)$
But, we know that
$\frac{d ^{2} y}{d t ^{2}} + ω^{2} Y = 0 ... (ii)$
Comparing both equation, we get
$ω^{2} = 2$
$\Rightarrow ω = 2$
The periodic time
$T = \frac{2 π}{ω} = \frac{2 π}{2}$
$= 2 π = π 2 s$