If a simple harmonic motion is represented by d t 2 d 2 x + a x = 0 , Its time period is,

The standard differential equation of a simple harmonic motion is given by d t 2 d 2 x + ω 2 x = 0 Comparing the given equation d t 2 d 2 x + a x = 0 with the standard equation, we get ω 2 = a ω = a The time period of simple harmonic motion is given by T = ω 2 π Substituting the value of ω , we get T = a 2 π Answer: a 2 π

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PhysicsSHMMiscellaneousEasy2 minPYQ_2026

PhysicsEasysingle choice

If a simple harmonic motion is represented by $\frac{d ^{2} x}{d t ^{2}} + a x = 0$ , Its time period is,

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Answer:

Solution:

The standard differential equation of a simple harmonic motion is given by

$\frac{d ^{2} x}{d t ^{2}} + ω^{2} x = 0$

Comparing the given equation $\frac{d ^{2} x}{d t ^{2}} + a x = 0$ with the standard equation, we get

$ω^{2} = a$

$ω = a$

The time period of simple harmonic motion is given by

$T = \frac{2 π}{ω}$

Substituting the value of $ω$ , we get

$T = \frac{2 π}{a}$

Answer: $\frac{2 π}{a}$

Stream:MHT_CET_MEDICALSubject:PhysicsTopic:SHMSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2026

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