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A simple pendulum performs simple harmonic motion about x=0 with an amplitude a and time period T. The speed of the pendulum at x=a/2 will be

Asked in CBSE AIPMT 2009 · v-x and a-x relations

• (1) (π a)/T
• (2) (3π²a)/T
• (3) (π a√3)/T
• (4) (π a√3)/(2T)

Step-by-step solution

Why the other options are wrong

• (1) comes from taking √a²-(a/2)² as a/2 instead of (a√3)/2: then v=(2π)/T×a/2=(π a)/T
• (2) comes from carries a stray π: v=ω√a²-x² brings in exactly one factor of (2π)/T, so the answer is linear in π, never quadratic
• (4) comes from using ω=π/T instead of (2π)/T, which halves the correct answer

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