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If a simple harmonic motion is represented by (d²x)/(dt²)+α x=0, its time period is

Asked in JEE Main 2005 · Force law, potential energy and circular projection

(1) 2πα
(2) 2π√α
(3) (2π)/α
(4) (2π)/(√α)

Answer: (4) (2π)/(√α)

Step-by-step solution

Comparing with the standard form (d²x)/(dt²)+ω²x=0 gives ω²=α.

T=(2π)/ω=(2π)/(√α).

Why the other options are wrong

(1) Multiplies by α instead of dividing, and never takes the square root.
(2) Takes ω=1/(√α), inverting the relation ω²=α.
(3) Identifies α with ω rather than with ω².

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