back to directory
NEET PHYSICSOscillationsEasy

Question

Two simple harmonic motions of angular frequencies 100100 and 1000 rad s−11000 \text{ rad s}^{-1} have the same displacement amplitude. The ratio of their maximum acceleration is:

A

1:101: 10

B

1:1021: 10^2

C

1:1031: 10^3

D

1:1041: 10^4

Step-by-Step Solution

  1. Identify Maximum Acceleration Formula: In Simple Harmonic Motion, the magnitude of maximum acceleration of a particle is given by amax=ω2Aa_{max} = \omega^2 A, where ω\omega is the angular frequency and AA is the amplitude .
  2. Set up Ratio: Let the two SHMs have angular frequencies ω1=100 rad s−1\omega_1 = 100 \text{ rad s}^{-1} and ω2=1000 rad s−1\omega_2 = 1000 \text{ rad s}^{-1}. They have the same amplitude, so A1=A2=AA_1 = A_2 = A.
  3. Calculate Ratio: Ratio=amax1amax2=ω12A1ω22A2\text{Ratio} = \frac{a_{max1}}{a_{max2}} = \frac{\omega_1^2 A_1}{\omega_2^2 A_2} Since A1=A2A_1 = A_2, this simplifies to: Ratio=(ω1ω2)2=(1001000)2\text{Ratio} = \left(\frac{\omega_1}{\omega_2}\right)^2 = \left(\frac{100}{1000}\right)^2 Ratio=(110)2=1100=1:102\text{Ratio} = \left(\frac{1}{10}\right)^2 = \frac{1}{100} = 1: 10^2

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Oscillations. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSOscillationssimpleharmonicmotionsangularfrequencies

More Oscillations Questions

View all

A simple pendulum performs simple harmonic motion about $x = 0$ with an amplitude $a$ and time period $T$. The speed of the pendulum at $x = rac{a}{2}$ will be:

A.$\frac{\pi a \sqrt{3}}{2T}$
B.$\frac{\pi a}{T}$
C.$\frac{3\pi^2 a}{T}$
D.$\frac{\pi a \sqrt{3}}{T}$
MediumSolve

The restoring force of a spring, with a block attached to the free end of the spring, is represented by:

A.
B.
C.4
D.$F = -kx$
EasySolve

The displacement-time ($x-t$) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2$ s is:

A.$-\frac{\pi^2}{16} \text{ ms}^{-2}$
B.$\frac{\pi^2}{8} \text{ ms}^{-2}$
C.$-\frac{\pi^2}{8} \text{ ms}^{-2}$
D.$\frac{\pi^2}{16} \text{ ms}^{-2}$
EasySolve

A particle executing simple harmonic motion has a kinetic energy of $K = K_0 \cos^2(\omega t)$. The values of the maximum potential energy and the total energy are, respectively:

A.$0$ and $2K_0$
B.$K_0/2$ and $K_0$
C.$K_0$ and $2K_0$
D.$K_0$ and $K_0$
MediumSolve

When two displacements represented by $y_1 = a \sin(\omega t)$ and $y_2 = b \cos(\omega t)$ are superimposed, the motion is:

A.not a simple harmonic
B.simple harmonic with amplitude a/b
C.simple harmonic with amplitude $\sqrt{a^2+b^2}$
D.simple harmonic with amplitude (a+b)/2
MediumSolve

From the given functions, identify the function which represents a periodic motion:

A.$e^{\omega t}$
B.$\log_e(\omega t)$
C.$\sin \omega t + \cos \omega t$
D.$e^{-\omega t}$
EasySolve

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then, its time period in seconds is:

A.\frac{\sqrt{5}}{\pi}
B.\frac{\sqrt{5}}{2\pi}
C.\frac{4\pi}{\sqrt{5}}
D.\frac{2\pi}{\sqrt{3}}
MediumSolve

Match List-I with List-II. **List-I (Graphs)** (a) Displacement-time graph with decreasing amplitude (Damped) (b) Displacement-time graph with constant amplitude (Undamped) (c) Force-displacement graph (Linear relationship, F = -kx) (d) Energy-time graph (Constant total energy) **List-II (Situations)** (i) Total mechanical energy is conserved (ii) Bob of a pendulum is oscillating under negligible air friction (iii) Restoring force of a spring (iv) Bob of a pendulum is oscillating along with air friction Choose the correct answer from the options given below:

A.(a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)
B.(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
C.(a)-(i), (b)-(iv), (c)-(iii), (d)-(ii)
D.(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
MediumSolve

Why 32,000+ students choose TopperSquare

Everything you need to crack NEET

15,000+ Chapter MCQs

Physics, Chemistry, Biology — chapter-wise, topic-wise practice

AI Performance Analytics

Know your weak topics. Get a personalised study plan.

Full NEET Mock Tests

180 questions, timed, with detailed score analysis

PYQ Sets 2010–2024

15 years of past papers with solved explanations

Start Practising Free

No credit card · 30-second signup · Free forever plan included

This neet physics practice question is part of the TopperSquare free question bank. TopperSquare offers 15,000+ chapter-wise NEET MCQs across Physics, Chemistry, and Biology with detailed step-by-step explanations, full mock tests, NEET PYQs (2010–2024), and an AI-powered performance analytics dashboard. browse all neet practice questions → · practice physics sets →

Explore more subjects:Physics MCQs•Chemistry MCQs•Biology MCQs•Botany MCQs•Zoology MCQs•NEET Mock Tests•NEET PYQs