(Solved): ( Problem 4 - Plot a decaying cosine wave 3 solutions submitted (max: Unlimited) | View my solutio ...

( Problem 4 - Plot a decaying cosine wave 3 solutions submitted (max: Unlimited) | View my solutions Problem Summary Damped oscillations are commonly used to describe physical systems such as mechanical vibrations and electrical circuits. The mathematical model to describe a damped oscillation is a cosine multiplied by an exponentionally decaying amplitude of the form: \( y(t)=A e^{-\alpha t} \cos (\omega t+\phi) \) where \( A \) is the initial amplitude with the same units as the physical quantity that is being modeled, \( \alpha \) is the damping constant in units inverse seconds, \( \omega \) is the radian frequency of the oscillation in radians/second, \( t \) is time in seconds, and \( \phi \) is the phase shift in radians. The period \( T \) of the wave is related to the radian frequency by the formula \[ T=\frac{2 \pi}{\omega} \text {. } \] Assume \( y(t) \) is a linear position measured in meters. Write a script that generates \( y \)-values for 200 equally spaced \( t \)-values spanning three periods of \( y(t) \) for a damped oscillation with the following parameter values: - \( A=10 \mathrm{~m} \) - \( a=0.25 \mathrm{~s}^{-1} \) - \( \omega=\pi / 2 \mathrm{rad} / \mathrm{s} \) - \( \phi=\pi / 4 \mathrm{rad} \) Assign the \( t \) values to a row vector variable tvalues. Assign the \( y(t) \) values to a row vector variable \( y \) values. Next use the plot command to generate a properly-labeled graph of \( y(t) \). Use MATLAB commands to add an appropriate title and axis labels to the figure. Solve this problem using vectorized code (i.e. use vectors and do not use a loop in your solution.) Previous Assessment: 4 of 6 Tests Passed ( \( 66 \%) \) \( \star \) Are the values assigned to tValues correct? (Pretest) Variable tValues must be of size [1 200]. It is currently of size [200 1]. Check where the variable is assigned a value. Be sure to use the built-in vlaue of \( \pi \) for full precision. (x) Are the values assigned to yValues correct? Variable yValues must be of size [1 200]. It is currently of size [200 1]. Check where the variable is assigned a value. Check the order of operations in your code to evaluate the formula.