A particle oscillates with simple harmonic motion. Its displacement from equilibrium is given by x(t) = 0.050 cos(10π t + π/4), where x is in meters and t is in seconds. What is the frequency of the oscillation?
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Correct answer
B. 5.0 Hz
Principle or equation
For simple harmonic motion x(t) = A cos(ωt + φ), the angular frequency ω = 2πf, where f is the frequency.
Why this answer is correct
From the equation, ω = 10π rad/s. Using ω = 2πf, we get f = ω/(2π) = (10π)/(2π) = 5.0 Hz.
Example
If x(t) = 0.10 cos(4π t), then ω = 4π rad/s and f = 2 Hz.
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