The position 7 (in meters) of a particle of mass m (in kilograms) is described as two perpendicular oscillations that are out of phase with each other: * = xẻi + yếa = cos(wt)ē1+ cos(wt+ $)ē2, where ø is the constant phase angle difference. a. Show that the position 7 of the particle satisfies the harmonic oscillator equation -w?r. dt? Compute the particle's velocity v = dī/dt, dot product 7 · v, and angular momentum L = mr x v. Is the angular momentum constant in both magnitude and direction? b. Set w = 2 rad / s and ø = 1/3 rad. Make a table with the following columns: t, x, y, Væ, Vy, and 7 · v 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 ro, Yo, VOr, VOy, and ro · vo Write down the spreadsheet formula for the first xo, Yo, VOx, 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 oscillations that are out of phase with each other: * = xẻi + yếa = cos(wt)ē1+ cos(wt+ $)ē2, where ø is the constant phase angle difference. a. Show that the position 7 of the particle satisfies the harmonic oscillator equation -w?r. dt? Compute the particle's velocity v = dī/dt, dot product 7 · v, and angular momentum L = mr x v. Is the angular momentum constant in both magnitude and direction? b. Set w = 2 rad / s and ø = 1/3 rad. Make a table with the following columns: t, x, y, Væ, Vy, and 7 · v 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 ro, Yo, VOr, VOy, and ro · vo Write down the spreadsheet formula for the first xo, Yo, VOx, Voy, and 7o · vo , assuming that the initial time to is spreadsheet cell A2.