Out of the following functions representing motion of a particle, which represents SHM? (I) y = sin(ωt) - cos(ωt); (II) y = sin³(ωt); (III) y = 5 cos(3π/4 - 3ωt); (IV) y = 1 + ωt + ω²t².
Options

Question

Out of the following functions representing motion of a particle, which represents SHM? (I) y = sin(ωt) − cos(ωt); (II) y = sin³(ωt); (III) y = 5 cos(3π/4 − 3ωt); (IV) y = 1 + ωt + ω²t².

G1 Physics · Accepted Answer

Step 1: A single sinusoid with constant frequency represents SHM. Step 2: (I) is a combination of same-frequency sine and cosine; it reduces to √2 sin(ωt − π/4). Step 3: (II) = [3sin(ωt) − sin(3ωt)]/4 contains two frequencies, so is not a single SHM. Step 4: (III) is a sinusoid of angular frequency 3ω. (IV) is a polynomial in time, not sinusoidal. Step 5: Hence only (I) and (III) represent SHM. Final answer: (B) (I) and (III).