The position of a 0.63-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos (πt/16). What is the maximum net force on the mass as it oscillates?
Question
The position of a 0.63-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos (πt/16). What is the maximum net force on the mass as it oscillates?
Solution
The maximum net force on a mass undergoing simple harmonic motion is given by the formula F = m*a_max, where m is the mass and a_max is the maximum acceleration.
The maximum acceleration in simple harmonic motion is given by a_max = ω²*x_max, where ω is the angular frequency and x_max is the maximum displacement.
From the equation of motion x = (0.160 m) cos (πt/16), we can see that x_max = 0.160 m.
The angular frequency ω is the coefficient of t in the argument of the cosine function, which is π/16 in this case.
So, a_max = (π/16)² * 0.160 m = 0.0195 m/s².
Substituting these values into the formula for the maximum force, we get F = 0.63 kg * 0.0195 m/s² = 0.0123 N.
So, the maximum net force on the mass as it oscillates is 0.0123 N.
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