The displacement time graph of a particle executing S.H.M. is given in figure :(sketch is schematic and not to scale) Which of the following statement is/are true for this motion? (A)    The force is zero at t=\frac{3T}{4}
(B)    The acceleration is maximum at t=T
(C)    The speed is maximum at t=\frac{T}{4}
(D)    The P.E. is equal to K.E. of the oscillation at t=\frac{T}{2}
Option: 1 (A) and (D)
Option: 2 (A), (B) and (C)
Option: 3 (B), (C) and (D)
Option: 4 (A), (B) and (D)

Answers (1)

From graph equation of SHM

X=ACos \omega t

A)

At  t=\frac{3T}{4}, the particle is at the mean position.

So  The force is zero at t=\frac{3T}{4}

B)

at T particle is at the extreme position so acceleration is maximum

C)

  The speed is maximum at t=\frac{T}{4}

because at t=\frac{T}{4} particle is at the mean position.

D)

\begin{array}{l} \mathrm{KE}=\mathrm{PE} \\ \frac{1}{2} \mathrm{k}\left(\mathrm{A}^{2}-\mathrm{x}^{2}\right)=\frac{1}{2} \mathrm{k} \mathrm{x}^{2} \\ \mathrm{~A}^{2}=2 \mathrm{x}^{2} \\ \mathrm{x}=\frac{+\mathrm{A}}{\sqrt{2}} \\ Using \ \frac{\mathrm{A}}{\sqrt{2}}=\mathrm{A} \text { cosot } \\ \mathrm{t}=\mathrm{T} / 8 \end{array}

So A, B and C are correct

Most Viewed Questions

Preparation Products

Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Test Series JEE Main 2024

Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 7999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2023

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, Faculty Support.

₹ 9999/- ₹ 6999/-
Buy Now
Knockout JEE Main (One Month Subscription)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, Faculty Support.

₹ 7999/- ₹ 4999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions