the general solution to a harmonic oscillator are related. There are two common forms for the general solution for the position of a harmonic oscillator as a function of time t: 1. x(t) = A cos (wt + p) and 2. x(t) = C cos (wt) + S sin (wt). Either of these equations is a general solution of a second-order differential equation (F= mā); hence both must have at least two--arbitrary constants--parameters that can be adjusted to fit the solution to the particular motion at hand. (Some texts refer to these arbitrary constants as boundary values.) Part D Find analytic expressions for the arbitrary constants A and in Equation 1 (found in Part A) in terms of the constants C and Sin Equation 2 (found in Part B), which are now considered as given parameters. Express the amplitude A and phase (separated by a comma) in terms of C and S. ► View Available Hint(s) A, O= IVE ΑΣΦ ?
the general solution to a harmonic oscillator are related. There are two common forms for the general solution for the position of a harmonic oscillator as a function of time t: 1. x(t) = A cos (wt + p) and 2. x(t) = C cos (wt) + S sin (wt). Either of these equations is a general solution of a second-order differential equation (F= mā); hence both must have at least two--arbitrary constants--parameters that can be adjusted to fit the solution to the particular motion at hand. (Some texts refer to these arbitrary constants as boundary values.) Part D Find analytic expressions for the arbitrary constants A and in Equation 1 (found in Part A) in terms of the constants C and Sin Equation 2 (found in Part B), which are now considered as given parameters. Express the amplitude A and phase (separated by a comma) in terms of C and S. ► View Available Hint(s) A, O= IVE ΑΣΦ ?
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Transcribed Image Text:the general solution to a harmonic oscillator are
related.
There are two common forms for the general
solution for the position of a harmonic oscillator as
a function of time t:
1. x(t) = A cos (wt + p) and
2. x(t) = C cos (wt) + S sin (wt).
Either of these equations is a general solution of a
second-order differential equation (F= mā);
hence both must have at least two--arbitrary
constants--parameters that can be adjusted to fit
the solution to the particular motion at hand. (Some
texts refer to these arbitrary constants as boundary
values.)
Part D
Find analytic expressions for the arbitrary constants A and in Equation 1 (found in Part A) in terms of the constants C and Sin
Equation 2 (found in Part B), which are now considered as given parameters.
Express the amplitude A and phase (separated by a comma) in terms of C and S.
► View Available Hint(s)
Α, φ =
V
ΑΣΦ
?
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