Frequency and Period of SHM AP Physics C Mechanics FRQ – Exam Style Questions etc.
Frequency and Period of SHM AP Physics C Mechanics FRQ
Unit 7: Oscillations
Weightage : 10-15%
Question
A uniform rod of mass M and length L is attached to a pivot of negligible friction as shown above. The pivot is located at a distance L/3 from the left end of the rod. Express all answers in terms of the given quantities and fundamental constants.
a. Calculate the rotational inertia of the rod about the pivot. The rod is then released from rest from the horizontal position shown above.
b. Calculate the linear speed of the bottom end of the rod when the rod passes through the vertical.
The rod is brought to rest in the vertical position shown above and hangs freely. It is then displaced slightly from this position by a small angle θ. Write the differential equation that governs the motion of the rod as it swings.
c. Calculate the period of oscillation as it swings, assuming that the angle of oscillation is small.
Answer/Explanation
Ans:
a. 
b. Conservation of energy
U = K
Mghcm = ½ Iω2
Mg(L/6) = ½ (ML2/9)(v/r)2 where r = 2L/3
solving gives v = 2(gL/3)1/2
c. T = 2π(I/mgd)1/2 where d = L/6
T = 2π((ML2/9)/(MgL/6))1/2 = 2π(2L/3g)1/2