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

  • Option 1)

    simple harmonic with amplitude \frac{a}{b}

  • Option 2)

    simple harmonic with amplitude \sqrt{a^{2}+b^{2}}

  • Option 3)

    not a simple harmonic 

  • Option 4)

    simple harmonic with amplitude \frac{a+b}{2}

 

Answers (1)

As we learnt in 

Superposition of sinusoidal wave -

y_{1}= Asin left ( kx-omega t 
ight )\y_{2}= Asin left ( kx-omega t +phi 
ight )

 

- wherein

Resultant equation is y= 2Acdot cos left ( phi /2 
ight )cdot sin left ( kx-omega t+frac{phi }{2} 
ight )

 

 y_{1}=a sinwt

y_{2}=b coswt=bsin(\omega t+\frac{\pi }{2})

y_{eq}=y_{1}+y_{2}

=a sin \omega t + b cos \omega t=a sin \omega t + b sin \left(\omega t+ \frac{\pi}{2}\right )

Since the frequencies for both S.H.M. are same resultant motion will be S.H.M.

A_{eq}=\sqrt{a^{2}+b^{2}+2 ab\ cos\frac{\pi}{2}}

A_{eq}=\sqrt{a^{2}+b^{2}


Option 1)

simple harmonic with amplitude \frac{a}{b}

Incorrect

Option 2)

simple harmonic with amplitude \sqrt{a^{2}+b^{2}}

Correct

Option 3)

not a simple harmonic 

Incorrect

Option 4)

simple harmonic with amplitude \frac{a+b}{2}

Incorrect

Most Viewed Questions

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
Knockout NEET 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout NEET 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series NEET 2021

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

₹ 6999/- ₹ 2999/-
Buy Now
Boost your Preparation for NEET 2021 with Personlized Coaching
 
Exams
Articles
Questions