First slide

Simple hormonic motion

Question

A particle executes simple harmonic "motion between x= - A and x = + A. The time taken by it to go from O to $\frac{A}{2}$ is T₁ and to go from A/2 to A is T₂. Then:

Moderate

A

$T_{1} < T_{2}$
B

$T_{1} > T_{2}$
C

$T_{1} = T_{2}$
D

$T_{1} = 2 T_{2}$

Solution

$Let x = A \sin ωt then A / 2 = A \sin {ωT}_{1}$
$\Rightarrow {ωT}_{1} = π / 6 \Rightarrow T_{1} = \frac{T}{6 ω} Also T_{2} = \frac{T}{4} - T_{1} = \frac{2 π}{4 ω} - \frac{π}{6 ω} = \frac{π}{3 ω} \Rightarrow T_{2} = 2 T_{1} \Rightarrow T_{2} > T_{1}$

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