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

Question

Hello,

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!

Answer 1

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.