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A particle performs SHM along a straight line between points M and N about mean position O. The amplitude is A (OM = ON = A). P is a point between O and N such that OP = PN = A/2. If t1 is the time taken by the particle to travel from M to P and t2 is the time taken from P to N, find t1/t2.

1. (a) 1
2. (b) 2
3. (c) 3
4. (d) 4

Correct answer: (b) 2

Solution

Set up origin at O. Particle starts at M (x = -A) at t = 0, so x(t) = -A cos(omega*t). Point P has OP = A/2, so x_P = +A/2 (between O and N). N has x_N = +A. Time t1: -A cos(omega*t1) = A/2 => cos(omega*t1) = -1/2 => omega*t1 = 2*pi/3 => t1 = T/3. Time for particle to reach N from M: -A cos(omega*t) = A => cos(omega*t) = -1 => omega*t = pi => t = T/2. So t2 = T/2 - T/3 = T/6. Therefore t1/t2 = (T/3)/(T/6) = 2.

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