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3. Pendulums approximately exhibit simple harmonic motion. Specifically, if we release a mass M suspended on a string of length I from a small angle (measured from the vertical), then the motion will approximately obey 0(t) = 0 cos(wt). Here w= √g/L is the angular frequency where g≈ 9.8 m/s² is the acceleration due to gravity (notice that √g/L has units of 1/time, so wt is just a number with no units). 1 L 1 M As with any simple harmonic motion, the period (time it takes to complete one cycle) is T = 2π/w and the frequency (number of cycles per unit time) is v= 1/T = w/2π. (a) Find a function (t) describing the motion of a 5 kg mass attached to a string of length 2.45 m released from an angle of 10° and use it to find the angle the object makes with the vertical after π/6 seconds. (b) Find the period and frequency for the system described in part (a). 0