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The function x = (6.0 m) cos [(3π rad/s)t+π/3 rad] gives the simple harmonic motion of a body. The speed as it passes through the equilibrium position is _____ m/s. Round your answer to the nearest tenth.

Question

The function x = (6.0 m) cos [(3π rad/s)t+π/3 rad] gives the simple harmonic motion of a body. The speed as it passes through the equilibrium position is _____ m/s. Round your answer to the nearest tenth.

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Solution

The speed of an object in simple harmonic motion as it passes through the equilibrium position is given by the formula v = ωA, where ω is the angular frequency and A is the amplitude.

From the given function, we can identify the amplitude A as 6.0 m and the angular frequency ω as 3π rad/s.

Substituting these values into the formula gives:

v = ωA = (3π rad/s)(6.0 m) = 18π m/s.

Rounding to the nearest tenth gives approximately 56.5 m/s.

This problem has been solved

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