When two displacements represented by y1 = a sin (ω t) and y2 = b cos (ω t) aresuperimposed the motion is (a) simple harmonic with amplitude √(a²+b²) (b) simple harmonic with amplitude ((a+b))/(2) (c) not a simple harmonic (d) simple harmonic with amplitude a/b

Answer: (a). y = asin ω t + bcos ω t = √(a²+b²) sin (ω t + φ) with tan φ = b/a. Same ω, so the result is SHM with amplitude √(a²+b²), answer (a).

When two displacements represented by y1 = a sin (ω t) and y2 = b cos… | NEET 2015 (AIPMT, Cancelled Paper)

Q14NEET 2015 · AIPMT · CANCELLED PAPEREasy

Damped, Forced Oscillations & Superposition

When two displacements represented by y1 = a sin $(\omega t)$ and y2 = b cos $(\omega t)$ aresuperimposed the motion is

Show answer and solution

Answer: (a)

$y = a\sin\omega t + b\cos\omega t = \sqrt{a^2+b^2}\,\sin(\omega t + \phi)$ with $\tan\phi = \frac{b}{a}$ .
Same $\omega$ , so the result is SHM with amplitude $\sqrt{a^2+b^2}$ , answer (a).

A simple harmonic oscillator of angular frequency 2 rad s ⁻¹ is acted upon by an external…JEE Main 2015 (10 Apr, Shift 1)
x and y displacements of a particle are given as x(t) = a sin ω t and y(t) = a sin2 ω t…JEE Main 2015 (10 Apr, Shift 1)
A pendulum with time period of 1s is losing energy due to damping. At certain time its…JEE Main 2015 (11 Apr, Shift 1)
A particle which is simultaneously subjected to two perpendicular simple harmonic motions…JEE Main 2014 (9 Apr, Shift 1)
The angular frequency of the damped oscillator is given by, ω = √((k/m-(r²)/(4m²))) where…JEE Main 2014 (11 Apr, Shift 1)
The amplitude of a simple pendulum, oscillating in air with a small spherical bob…JEE Main 2014 (9 Apr, Shift 1)
Bob of a simple pendulum of length l is made of iron. The pendulum is oscillating over a…JEE Main 2013 (23 Apr, Shift 1)
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5…JEE Main 2013