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When a spring oscillates with decreasing amplitude (because it is being damped by friction, for example), its motion is often modeled as the product of a trigonometric function (the oscillation) and an exponential function (the decay of amplitude). Suppose that the displacement of a particular damped spring is s(t): -1.8t cos(2πt), with s in inches and t in seconds. = 2e a) Find the spring's velocity with respect to t: v(t) = -4 pi ^(-1.8t) sin(2 pi t)-3.6e^(-1.8t)cos(2 pi t) That's not it. in/sec .-1.8t -4π sin(2πt) — 3.6e-1.8t Preview v(t) = cos (2π t) . in/sec

When a spring oscillates with decreasing amplitude (because it is being damped by friction, for example), its motion is often modeled as the product of a trigonometric function (the oscillation) and an exponential function (the decay of amplitude). Suppose that the displacement of a particular damped spring is s(t): -1.8t cos(2πt), with s in inches and t in seconds. = 2e a) Find the spring's velocity with respect to t: v(t) = -4 pi ^(-1.8t) sin(2 pi t)-3.6e^(-1.8t)cos(2 pi t) That's not it. in/sec .-1.8t -4π sin(2πt) — 3.6e-1.8t Preview v(t) = cos (2π t) . in/sec

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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When a spring oscillates with decreasing amplitude (because it is being damped by friction, for example), its motion is often modeled as the product of a trigonometric function (the oscillation) and an exponential function (the decay of amplitude). Suppose that the displacement of a particular damped spring is s(t) 2e-1.8t cos(2πt), with s in inches and t in seconds. a) Find the spring's velocity with respect to t: v(t) = -4 pi ^(-1.8t) sin(2 pi ! t)-3.6e^(-1.8t) cos(2 pi t) That's not it. in/sec .-1.8t -4π¯¯ = -1.8t sin(2πt) — 3.6e¯ Preview v(t) = cos(2π. t) in/sec
Transcribed Image Text:When a spring oscillates with decreasing amplitude (because it is being damped by friction, for example), its motion is often modeled as the product of a trigonometric function (the oscillation) and an exponential function (the decay of amplitude). Suppose that the displacement of a particular damped spring is s(t) 2e-1.8t cos(2πt), with s in inches and t in seconds. a) Find the spring's velocity with respect to t: v(t) = -4 pi ^(-1.8t) sin(2 pi ! t)-3.6e^(-1.8t) cos(2 pi t) That's not it. in/sec .-1.8t -4π¯¯ = -1.8t sin(2πt) — 3.6e¯ Preview v(t) = cos(2π. t) in/sec
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