SATHEE: Oscillations - Result Question 18

Oscillations - Result Question 18

21. Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along $x$ and $y$ axis. If the two amplitudes are equal and the phase difference is $π / 2$ , the resultant motion will be

[1997]

(a) a circle

(b) an ellipse with the major axis along y-axis

(d) a straight line inclined at $45^{\circ}$ to the $x$ -axis

Show Answer

Answer:

Correct Answer: 21. (a)

Solution:

(a) Equation of two simple harmonic motions

$\begin{aligned} (1) & y = A \sin (ω t + ϕ) \\ x = A \sin (ω t + ϕ + \frac{π}{2}) \\ (2) & \Rightarrow x = A \cos (ω t + ϕ) \end{aligned}$

On squaring and adding equations (1) and (2), $x^{2} + y^{2} = A^{2}$

This is an equation of a circle. Hence, resulting motion will be a circular motion.

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Oscillations - Result Question 18

21. Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will be

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

21. Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along $x$ and $y$ axis. If the two amplitudes are equal and the phase difference is $π / 2$ , the resultant motion will be