SATHEE: Oscillations - Result Question 22

Oscillations - Result Question 22

25. The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $π$ results in the displacement of the particle along [1990]

(a) circle

(b) figures of eight

(d) ellipse

Show Answer

Answer:

Correct Answer: 25. (c)

Solution:

or, $\frac{x}{a} = - \frac{y}{b}$ or $y = - \frac{b}{a} x$

It is an equation of a straight line.

If two mutually perpendicular S.H.M’s of same frequency be $x = 9$ , sin $ω t$ and $y = a_{2} \sin (ω t + ϕ)$ then general equation of Lissajous figure is

$\begin{aligned} \frac{x^{2}}{a_{1}^{2}} + \frac{y_{2}}{a_{2}^{2}} - \frac{2 x y}{a_{1} a_{2}} \cos ϕ = \sin^{2} ϕ \\ For ϕ = π \frac{x^{2}}{a_{1}^{2}} + \frac{y^{2}}{a_{2}^{2}} - \frac{2 x y}{a_{1} a_{2}} \cos (π) = \sin 2 (π) \\ \Rightarrow \frac{x}{a_{1}} + \frac{y}{a_{2}} = 0 \frac{x}{a} + \frac{y}{a^{2}} = 0 \Rightarrow y = \frac{- a_{2}}{a_{1}} x \end{aligned}$

Oscillations - Result Question 22

25. The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $π$ results in the displacement of the particle along [1990]

Answer:

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Oscillations - Result Question 22

25. The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of π results in the displacement of the particle along [1990]

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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25. The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $π$ results in the displacement of the particle along [1990]