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A mass on the end of a spring is oscillating with angular
Chapter 5, Problem 5.6(choose chapter or problem)
A mass on the end of a spring is oscillating with angular frequency \(\omega\). At t = 0, its position is \(x_{0}>0\) and I give it a kick so that it moves back toward the origin and executes simple harmonic motion with amplitude \(2 x_{0}\). Find its position as a function of time in the form (III) of Problem 5.5.
Questions & Answers
QUESTION:
A mass on the end of a spring is oscillating with angular frequency \(\omega\). At t = 0, its position is \(x_{0}>0\) and I give it a kick so that it moves back toward the origin and executes simple harmonic motion with amplitude \(2 x_{0}\). Find its position as a function of time in the form (III) of Problem 5.5.
ANSWER:Step 1 of 4
The equation of simple harmonic motion is given as:
\(x(t)=A \cos (\omega t-\delta) \ldots \ldots(1)\)
At \(t=0\) the position is \(x_{0}\). Therefore, the above equation can be written as:
\(\begin{aligned}
x_{0} & =A \cos (-\delta) \\
& =A \cos \delta
\end{aligned}\)