The displacement of a particle executing SHM at any instant t is x-asin- t- The acceleration of the particle at t-T-4 will be

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Wave Equation

The displacem...

Question

The displacement of a particle executing SHM at any instant t is $x = a sin ω t$ . The acceleration of the particle at $t = \frac{T}{4}$ will be

a ω

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a ω^{2}

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- a ω

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- a ω^{2}

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Solution

The correct option is B $- a ω^{2}$
$T = 2 π / ω$ , thus $T / 4 = π / 2 ω$
Thus, $x = A s i n ω t = A s i n ω (π / 2 ω) = A s i n π / 2 = A$
Thus, $a = - ω^{2} x = - ω^{2} A$

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The displacement of a particle executing SHM at any instant t is x=asinωt. The acceleration of the particle at t=T4 will be

The correct option is B −aω2T=2π/ω, thus T/4=π/2ωThus, x=Asinωt=Asinω(π/2ω)=Asinπ/2=AThus, a=−ω2x=−ω2A

The displacement of a particle executing SHM at any instant t is $x = a sin ω t$ . The acceleration of the particle at $t = \frac{T}{4}$ will be

The correct option is B $- a ω^{2}$
$T = 2 π / ω$ , thus $T / 4 = π / 2 ω$
Thus, $x = A s i n ω t = A s i n ω (π / 2 ω) = A s i n π / 2 = A$
Thus, $a = - ω^{2} x = - ω^{2} A$