Question: Hi, I was hoping you could please help me or point me in the right direction with the fourier series hand calculations of the following question;

A stamping machine involving cyclic punching of sheet metals; if the position of the sliding block along the x direction is 𝑥(𝑡). If the position of the sliding block along the 𝑥(𝑡) direction in one period of time is given by the function:

𝑥(𝑡) = 𝑟 (1 − cos(𝜃 − 𝜓))

where 𝑟 is the radius, 𝜃 is the angular displacement related to the position of the sliding block, and 𝜓 is the phase shift. Based on one revolution corresponding to 6.28 sec, 𝜃 ≈ 𝑡, express 𝑥(𝑡) = 𝑟 (1 − cos(𝑡 − 𝜓)) as a trigonometric Fourier series; then plot the signal harmonics and the recovered signal 𝑥(𝑡).

Thankyou  Edit