Arbitrary constants in Two General Simple Harmonic Motion Solutions

Question

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(omega*t phi)

and

2. x(t) = C*cos(omega*t) S*sin(omega*t)

Either of these equations is a general solution of a second-order differential equation F = m*a; 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.)

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What are the arbitrary constants in Equation 1?

A: omega only

B: A only

C: A and phi

D: A and omega

E: omega and phi

F: A and omega and phi

Answer 1

C: A and phi

C and S would be the correct answer if the question asked for the constants in equation 2.

Answer 2

the constants are:

either: 1)A and phi;

or: 2)C and S;

thus your answer is C;