The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t = 4/3 s is

Question

The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t = 4/3 s is (A) (√3/32)π2cm/s2 (B) (-π2/32)cm/s2 (C) (π2/32)cm/s2 (D) -(√3/32)π2 cm/s2

Tardigrade Admin · Accepted Answer

T=8 s, ω=(2 π/T)=((π/4)) rads -1 ⇒ x=A sin ω t ∴ a=-ω2 x=-((π2/16)) sin ((π/4) t) Substituting t=(4/3) s, we get a=-((√3/32) π2) cms -2

Q. The $x - t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t = 4/3 s$ is

$\frac{3}{32} π^{2} c m / s^{2}$

$\frac{- π ^{2}}{32} c m / s^{2}$

$\frac{π ^{2}}{32} c m / s^{2}$

$- \frac{3}{32} π^{2} c m / s^{2}$

$T = 8 s, ω = \frac{2 π}{T} = (\frac{π}{4}) r a d s^{- 1}$
$\Rightarrow x = A sin ω t$
$∴ a = - ω^{2} x = - (\frac{π ^{2}}{16}) sin (\frac{π}{4} t)$
Substituting $t = \frac{4}{3} s$ , we get
$a = - (\frac{3}{32} π^{2}) c m s^{- 2}$

Q. The x−t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t=4/3s is

323​​π2cm/s2

32−π2​cm/s2

32π2​cm/s2

−323​​π2cm/s2