(Solved): Comparing the general equation \( x=A \cos (\omega t+\varphi) \) with the given equation, \( x=3.0 ...

Comparing the general equation \( x=A \cos (\omega t+\varphi) \) with the given equation, \( x=3.00 \cos (7.00 \pi t+\pi) \), we can solve for frequency, period, amplitude, phase constant, and position. (a) From the given equation, and the equation that relates angular frequency to frequency, we have \[ \omega=2 \pi f=\pi \mathrm{rad} / \mathrm{s} . \] Solving for the frequency, \[ f=\quad \mathrm{Hz} . \] (b) For the period, we have \[ T=\frac{1}{f}= \] (c) For the amplitude, we have \[ A=\quad \mathrm{m} \text {. } \] (d) For the phase constant, we have \[ \begin{aligned} \varphi & =\pi \mathrm{rad} \\ & = \end{aligned} \] Part 4 of 4 - Analyze (e) At \( t=0.280 \mathrm{~s} \), A calculator can be set to work in either radians or degrees. We should get the same answer with either setting within any rounding done in converting between the two angular measures. By convention, when the angle in the trig function is given without units, it is assumed to be in radians.