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Question:

Which of the following equation does not represent a SHM?

sinωt-cosωt

cosωt+sinωt

1-sin²ωt

sinωt+cos(ωt+α)

Solution:

For an equation to represent an SHM, it must satisfy d²x/dt² = -kx
Consider option C, x = 1-sin²ωt ⇒ d²x/dt² = 4ω²sin2ωt
which cannot be expressed as c(1-sin²ωt) where c is a constant.
Hence this does not represent an SHM.