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How long will it take for this hanging mass to return to the zero angle?


I'm taking a summer course in college physics and am reviewing some practice questions to prepare for my oncoming exam. I'd really appreciate some help on this question that I'm not sure about.

A 0.1 kg mass suspended from a 1 meter long string is released with an amplitude of 20 degrees from a zero vertical angle. How long will it take for the mass to return to the zero angle?

Thanks in advance for any assistance!
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1 Answer

There is a formula for the period of a pendulum:
T ≈ 2π √(L / g)
Where T is the period
L is the length of the string -- 1 m
g is the acceleration of gravity -- 9.8 m/s2
This is an APPROXIMATE formula.  There is no EXACT finite formula for the period, but when the angle is small (and 20° counts as small enough), the approximation is very good.
So in this case you get:
T = 2π √(1 / 9.8) = 2.00 s
Now that's the period of an entire oscillation, which consists of 4 equal parts:
1. From 20° to vertical
2. From vertical to 20° in the opposite direction
3. From 20° back to vertical
4. From vertical back to the original position
Each segment takes the same amount of time, which means that it takes 2 s / 4 = 0.5 s for the mass to initially return to vertical, or the zero angle.