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

You visited us 7 times! Enjoying our articles? Unlock Full Access!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a ω^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- a ω

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- a ω^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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, $a = - ω^{2} x = - ω^{2} A$

Suggest Corrections

Similar questions

The displacement of a particle moving in S.H.M. at any instant is given by y = a sin $ω t$ . The acceleration after time $t = \frac{T}{4}$ is (where T is the time period) [MP PET 1984]

Q. The displacement of a particle executing SHM at any instant t is

x = 0.01 sin 100 (t + 0.05)

then its time period will be

Q. The displacement of a particle executing simple harmonic motion at any instant t is

x = 3 cos 2 π t

. The acceleration produced in the particle will be:

Q. Two particles are executing SHM. Their displacements at any instant of time t are

x = a sin (ω t - ϕ)

and

y = b cos (ω t - ϕ)

. The phase difference between them will be:

Q. The displacement of a particle executing SHM at any instant t is

x = 7 cos 0.5 π t

. The time taken by the particle in reaching from mean position to extreme position will be

Join BYJU'S Learning Program

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, $a = - ω^{2} x = - ω^{2} A$