The position 7 (in meters) of a particle of mass m (in kilograms) is described as two perpendicular ocillations that are out of phase with each other: * = xẻi + yế = cos(wt)ei + cos(wt + ¢)e2, where ø is the constant phase angle difference. a. Show that the position 7 of the particle satisfies the harmonic oscillator equation dt2 Compute the particle's velocity i = dĩ/dt, dot product 7 · v, and angular momentum L = mĩ x v. Is the angular momentum constant in both magnitude and direction? b. Set w = 2 rad / s and ø = T/3 rad. Make a table with the following columns: t, x, y, Vz, Vy, and 7 · Put the units beside their respective variables and enclose the units inside the parentheses. Set the initial time to be to = 0 and use the spreadsheet to compute the values of xo, yo, VOx, VOy, and ro · vo Write down the spreadsheet formula for the first æ0, Yo, VOz, VOy, and 7o · vo , assuming that the initial time to is spreadsheet cell A2.

The position 7 (in meters) of a particle of mass m (in kilograms) is described as two perpendicular ocillations that are out of phase with each other: * = xẻi + yế = cos(wt)ei + cos(wt + ¢)e2, where ø is the constant phase angle difference. a. Show that the position 7 of the particle satisfies the harmonic oscillator equation dt2 Compute the particle's velocity i = dĩ/dt, dot product 7 · v, and angular momentum L = mĩ x v. Is the angular momentum constant in both magnitude and direction? b. Set w = 2 rad / s and ø = T/3 rad. Make a table with the following columns: t, x, y, Vz, Vy, and 7 · Put the units beside their respective variables and enclose the units inside the parentheses. Set the initial time to be to = 0 and use the spreadsheet to compute the values of xo, yo, VOx, VOy, and ro · vo Write down the spreadsheet formula for the first æ0, Yo, VOz, VOy, and 7o · vo , assuming that the initial time to is spreadsheet cell A2.