Match each time-dependent function in List I with the correct description in List II.
List I:
A. sin²(ωt)
B. sin³(2ωt)
C. sin(ωt)+cos(πωt)
D. cos(ωt)+cos(2ωt)
List II: I. Periodic with period π /ω, but not simple harmonic motion II. Periodic with period 2π /ω, but not simple harmonic motion III. Periodic with period π /ω and represents simple harmonic motion about its mean position IV. Non-periodic
Choose the correct matching.

Question

Match each time-dependent function in List I with the correct description in List II.

List I:
A. sin²(ωt)
B. sin³(2ωt)
C. sin(ωt)+cos(πωt)
D. cos(ωt)+cos(2ωt)

List II: I. Periodic with period π /ω, but not simple harmonic motion II. Periodic with period 2π /ω, but not simple harmonic motion III. Periodic with period π /ω and represents simple harmonic motion about its mean position IV. Non-periodic

Choose the correct matching.

G1 Physics · Accepted Answer

For A: sin²(ωt) = (1 ÷ 2)-(1 ÷ 2)cos(2ωt). It is a single sinusoidal variation about the mean value 1 ÷ 2 and has period T = π ÷ ω. Thus A → III. For B: sin³(2ωt) = (3 ÷ 4)sin(2ωt)-(1 ÷ 4)sin(6ωt). The common period is π ÷ ω, but the motion contains more than one angular frequency, so it is not SHM. Thus B → I. For C, the two angular frequencies are ω and πω. Their ratio π is irrational, so there is no common period. Thus C → IV. For D, the terms cos(ωt) and cos(2ωt) have common period 2π ÷ ω,…