A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 5.0 cm.If a timer is started when its displacement is a maximum (hence x = 5 cm when t = 0),what is the acceleration magnitude when t = 3 s? A) 31.6 m/s² B) 15.8 m/s² C) 10.5 m/s² D) zero

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Quizplus · Accepted Answer

The acceleration in simple harmonic motion is given by a(t) = -ω²x(t). The angular frequency ω = 2πf = 8π rad/s. At t = 3 s, x(t) = A cos(ωt) = 5 cm cos(8π * 3) = 5 cm. Thus, a(t) = -(8π)² * 0.05 m = 31.6 m/s².

A Mass on a Spring Vibrates in Simple Harmonic Motion