Which of the following combinations of variables results in the greatest period for a pendulum? length = l, mass = m, and maximum angular displacement = degrees length = l, mass = m, and maximum angular displacement = 3 degrees length = 2l, mass = m/2, and maximum angular displacement = 1 degree length = 1.5l, mass = 2m, and maximum angular displacement = 2 degrees length = l, mass = 4m, and maximum angular displacement = 4 degrees

length = 2L, mass = M/2, and maximum angular displacement = 1 degree

Explanation:

We consider only small amplitude oscillations (like in this case), so that the angle θ is always small enough. Under these conditions recall that the equation of motion of the pendulum is:

And its solution is:

Where are the angular frequency of the oscillations, from which we determine their period:

Therefore the period of a pendulum will only depend on its length, not on its mass or angle, for angles small enough. So, the answer is the one with the greater length.

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