NEED HELP ON PART C! You drill a hole at the end of a solid thin rod of length 2

Question

NEED HELP ON PART C!

You drill a hole at the end of a solid thin rod of length 2.6 m, and then attach the rod through this hole onto an approximately frictionless pivot. At t=0, you release the rod from rest at a small angle of 40 from vertical, so that it executes simple harmonic motion.

a.) What will be its oscillation period?
2.64 s answer is correct

b.) When released, how high is the center of mass of the pendulum, above its lowest point during the oscillation?
3.17 mm answer is correct

c.) What is the maximum angular speed of the pendulum during its oscillation?
max = ______rad/s (NOT 1.878 rad/s, 2.38 rad/s, or 4.99 rad/s)
and at what time does this first occur? _____ s (NOT 0.57 s, 0.60 s, or 0.32 s)

Also, find the maximum linear speeds of:
the pendulum's center of mass: ____________m/s (NOT 4.99 m/s, 6.19 m/s, 2.446 m/s)
the lowest point of the pendulum: _____________ m/s (NOT 4.99 m/s, 3.09 m/s, 4.883 m/s)

Explanation / Answer

c. assuming the centre of mass of the rod to be at the centre of the rod
Loss in PE = mg*l(1-cos(40))/2 = gain in ke = mv^2/2
v = 2.441 m/s [ linear velo of com]
v = 4.8831 m/s [ linear velo of endpoint]
w = 2.441/1.3 = 0.81366 [ angular velocity]
this first occurs at 2.64/4 = 0.66 s

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