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
$a ω^{2}$
$- a ω^{2}$
$- a ω$
$a ω$

Question

The displacement of a particle executing SHM any instant t is x-asin-omega t- The acceleration of the particle displaystyle t-frac-T-4- will beaomega-2-aomega-2-aomegaaomega

Toppr Admin · Accepted Answer

T-2-x3C0-x3C9- thus T-4-x3C0-2-x3C9-Thus- x-Asin-x3C9-t-Asin-x3C9-x3C0-2-x3C9-Asin-x3C0-2-AThus- a-x2212-x3C9-2x-x2212-x3C9-2A

The displacement of a particle executing SHM at any instant t is x=asinωt. The acceleration of the particle at t=T4 will beaω2−aω2−aωaω

T=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
$a ω^{2}$
$- a ω^{2}$
$- a ω$
$a ω$

$T = 2 π / ω$ , 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, $a = - ω^{2} x = - ω^{2} A$