[120]A building is being shaken by a periodic force f(t) defined by f(t)=\left\{\begin{array}{cc} -C t, & -\frac{\pi}{A} \leq t<0 \\ C t, & 0 \leq t<\frac{\pi}{A} \end{array}\right. Insert the values

of YOUR parameters A and C for YOUR force f (t). State the period of f(t). Sketch f(t) over the domain State with reason(s) whether the function is odd, even, or neither. Determine and write down the first four non-zero terms in the Fourier series for f(t) and state the frequency with the largest amplitude.[60] Write down the first four non-zero coefficients in the Fourier series for g(t)=\left\{\begin{array}{rl} -C t-\frac{C \pi}{2 A}, & -\frac{\pi}{A} \leq t<0 \\ C t-\frac{C \pi}{2 A}, & 0 \leq t<\frac{\pi}{A} \end{array}, \quad g\left(t+\frac{2}{A} \pi\right)=g(t)\right. (c)Write down the Fourier series for cos2(2ACT) and briefly explain the reason for your answer.[20]