A 1 kg particle undergoes simple harmonic motion with period T = 20 s. At t = 0 it crosses the mean position with velocity pi cm/s. Which of the following statements is/are correct?

the maximum acceleration of the particle is 10 cm/s²
when it is 4 cm from the mean position, its velocity is 6*pi/10 cm/s
the kinetic energy of the particle when its displacement is 5 cm from the mean position is 3*pi²/(8*10⁶) J
its velocity at displacement 6 cm from the mean position is 8*pi/10 cm/s

Correct answer: its velocity at displacement 6 cm from the mean position is 8*pi/10 cm/s

Solution

With omega = pi/10 rad/s and A = 10 cm: max acceleration = omega²*A = pi²/10 cm/s² (not 10), so A is wrong. At x=6 cm: v = (pi/10)*sqrt(100-36) = (pi/10)*8 = 8*pi/10 cm/s, confirming option D.

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