1 answer

How do you find the amplitude for #y(t) = 1/4e^-t cos6t#?

Question:

How do you find the amplitude for #y(t) = 1/4e^-t cos6t#?

Answers

In this damped oscillation, as in springs, the amplitude
#(1/4 e^(- t )) darr# as #t uarr#. See graphs for both the oscillation and the diminishing amplitude.

Explanation:

In the amplitude-damping periodic oscillation,

#y = (1/4e^(-t)) cos 6t, t >= 0#,

t-intercepts;# ( 2k + 1 ) pi/2# ( from zeros of #cos 6t# ,

#k = 0, 1, 2, 3, ...#

the amplitude #a ( t ) = 1/4e^(-t)#

is a function of time t that #darr#, as #t uarr#.

The period is #(2pi)/6 = pi/3#.

See the second graph, for the exponential decay of amplitude..
graph{y-1/4e^(-x) cos (8x) = 0[0 6 -1.5 1.5]}
Amplitude-decay graph:
graph{(y-1/4e^(-x))(y-0.04) = 0[0 5 0 1]}

See just one-in-many referenceas:

https://deutsch.physics.ucsc.edu/6A/book/harmonic/node18.html

.

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