Physics · Oscillations · NEET
Yes. Both terms have the same angular frequency w. Their sum can be rewritten as a single term R sin(wt + phi). Any motion of the form R sin(wt + phi) is SHM, so the sum is SHM with the same frequency w and time period T = 2 pi / w. Only the amplitude and starting phase change, not the frequency.
Because sin wt and cos wt reach their maximum values at different times. Sine is maximum when cosine is zero, and cosine is maximum when sine is zero. So the two peaks never add up at the same moment. Think of them as two sides at right angles: you combine them like a right triangle, giving the hypotenuse R = root(A squared + B squared), never the plain sum A + B.
Write A sin wt + B cos wt = R sin(wt + phi). Expand the right side: R sin wt cos phi + R cos wt sin phi. Match terms: A = R cos phi and B = R sin phi. Divide them: tan phi = B/A, so phi = tan inverse (B/A). Squaring and adding gives R = root(A squared + B squared).
No. A0 is a fixed number added to every position. It only shifts the mean (centre) position of the oscillation up or down. The particle still swings the same distance about this new centre, so the amplitude stays R = root(A squared + B squared). A0 is not part of the amplitude.
Then the simple formula does NOT apply. R = root(A squared + B squared) works ONLY when both terms share the SAME angular frequency w. With different frequencies the motion is not simple harmonic and has no single fixed amplitude.
The displacement of a particle executing simple harmonic motion is y = A0 + A sin wt + B cos wt. The amplitude of its oscillation is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is R = root(A squared + B squared). This single amplitude describes the combined simple harmonic motion, which has the same frequency as the two parts.
The phase constant is phi = tan inverse (B/A), found by writing the sum as R sin(wt + phi) and matching the sine and cosine coefficients.
Yes, as long as both terms have the same angular frequency w. The sum equals R sin(wt + phi), which is SHM with time period T = 2 pi / w.
It is root(3 squared + 4 squared) = root(9 + 16) = root 25 = 5 units. The common trap answer 7 (from 3 + 4) is wrong.
Yes. You can write A sin wt + B cos wt = R cos(wt - alpha) with the same R = root(A squared + B squared). Only the phase reference changes; the amplitude is identical.
