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What is SHM? Show that in SHM acceleration is directly proport

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What is SHM? Show that in SHM acceleration is directly proportional to its displacement at a give instant.

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Text solutionVerified

Simple Harmonic Motion is a type of motion in which displacement is always directed towards mean position and acceleration is directly proportional to displacement and opposite in direction.
Let a

SHm

be represented by

x = A sin ω t

\Rightarrow \frac{d x}{d t} = A ω cos ω t

\Rightarrow \frac{d ^{2} x}{d t ^{2}} = - A ω^{2} sin^{2} ω t

\Rightarrow \frac{d ^{2} x}{d t ^{2}} = - ω^{2} x

Now

\frac{d ^{2} x}{d t ^{2}} = α =

acceleration

\Rightarrow a = - ω^{2} x

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Question Text	What is SHM? Show that in SHM acceleration is directly proportional to its displacement at a give instant.
Topic	Oscillations
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	110

What is SHM? Show that in SHM acceleration is directly proportional to its displacement at a give instant.

Text solutionVerified

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