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A rigid rod of fixed length ℓ has its ends A and B constrained to slide along the x-axis and y-axis, respectively. The angular speed of the rod is constant, with dθ/dt = 2 rad s⁻¹ at all times. A point P is fixed on the rod, and M is the foot of the perpendicular from P onto the x-axis. During the interval in which θ increases from 0 to π/2, which statement is true?

1. The acceleration of M is always directed to the right
2. M performs simple harmonic motion
3. M travels with uniform speed
4. M has constant acceleration

Correct answer: M performs simple harmonic motion

Solution

The foot M tracks the x-coordinate of P, which equals a*cos(theta). Since dtheta/dt is constant, theta = w*t and x_M = a*cos(w*t), so M executes simple harmonic motion.

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