A particle starts from a point P at a distance of A /2 from the mean position O and travels towards left as shown in the figure. If the time period of SHM, executed about O is T and amplitude A then t

Question

A particle starts from a point P at a distance of A /2 from the mean position O and travels towards left as shown in the figure. If the time period of SHM, executed about O is T and amplitude A then the equation of motion of particle is :

TestHub · Accepted Answer

Particle starts at x = +A/2 moving left (towards -x).

Sine form: $x = A sin (\frac{2 π}{T} t + ϕ)$ : at t = 0, $sin ϕ = \frac{1}{2}$ and $v = A ω cos ϕ < 0 \Rightarrow ϕ = \frac{5 π}{6}$ so (B) is correct.

Cosine form: $x = A cos (\frac{2 π}{T} t + ϕ)$ : $cos ϕ = \frac{1}{2}$ and $v = - A ω sin ϕ < 0 \Rightarrow ϕ = \frac{π}{3}$ so (D) is correct.

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