The position of a mass oscillating at the end of a spring is s(t) = A sin ωt, where A is the amplitude and ω is the angular frequency. Show that the speed |v(t)| is at a maximum when the acceleration a(t) is zero and that |a(t)| is at a maximum when v(t) is zero.
The position of a mass oscillating at the end of a spring is s(t) = A sin ωt, where A is the amplitude and ω is the angular frequency. Show that the speed |v(t)| is at a maximum when the acceleration a(t) is zero and that |a(t)| is at a maximum when v(t) is zero.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 26E
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The position of a mass oscillating at the end of a spring is s(t) = A sin ωt, where A is the amplitude and ω is the angular frequency. Show that the speed |v(t)| is at a maximum when the acceleration a(t) is zero and that |a(t)| is at a maximum when v(t) is zero.
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