# Periodic Motion TBR #1 Question

#### glam407

##### Full Member
Question: If at the lowest point of its arc Mass M has a velocity of ten meters per second, then at how many points in time during the period of one complete cycle does the pendulum have a speed of five meters per second?

And the explanation says it goes back and forth (once each time) = 2 total times, and there are two points where there are 5 m/s ....but I don't understand how there are two points where it's 5 m/s?

#### Jepstein30

##### Full Member
Question: If at the lowest point of its arc Mass M has a velocity of ten meters per second, then at how many points in time during the period of one complete cycle does the pendulum have a speed of five meters per second?

And the explanation says it goes back and forth (once each time) = 2 total times, and there are two points where there are 5 m/s ....but I don't understand how there are two points where it's 5 m/s?

It is going 10 m/s at the bottom of the arc. We also know it is swinging back and forth like a pendulum. This means that at the top of its arc, it reverses direction. For it to reverse direction, there needs to be one moment in there with velocity of 0. So it's going from 10 m/s to 0 m/s, must be 5 m/s at some point. Likewise, as it comes from the top of the arc back to the bottom, it is also going from 0 to 10 m/s.. again passing 5 m/s for some split second.

For one complete cycle: Start at the top of the left arc:
0 to 10 on the way down
10 to 0 on the way up to the right
0 to 10 on the way down
10 to 0 on the way up to the left

One cycle, 4 times passing 5 m/s. For some minute time period, the mass has to be moving at 5 m/s.

EDIT: Just realized this question is actually pretty good. If you notice, it is asking for SPEED, not velocity. If it were asking for velocity, only twice would it hit 5 m/s (the other two would be -5 m/s) but since it is asking for speed, direction doesn't matter.

#### BerkReviewTeach

##### Company Rep & Bad Singer
Vendor
10+ Year Member
The big thing here is distinguishing between points in space and points in time in a single cycle.

#### Ibn Alnafis MD

##### Full Member
10+ Year Member
The big thing here is distinguishing between points in space and points in time in a single cycle.

Exactly.

I missed this question because I overlooked "the point in time" and though there are only two points in space at which the pendulum speed is 5 m/s.

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