Question

The graph shows the distance y, in centimeters, a pendulum moves to the right (positive displacement) and to the left (negative displacement), for a given number of seconds x.
How many seconds are required for the pendulum to swing from its position furthest to the right to its position furthest to the left?

Answer 1

Time required for the pendulum to swing from its position furthest to the right to its position furthest to the left: 1.25 seconds

Step-by-step explanation:

A pendulum is a system consisting of a rod/string connected to a mass which is left free to oscillate back and forth around its equilibrium position, straight vertical.

The period of a pendulum is the time the pendulum takes to complete one full oscillation, that means it is the time the pendulum takes to go from its furthest position on the left to the same position again. It is calculated as

$T=2\pi \sqrt{\frac{L}{g}}$

where L is the length of the pendulum and g the acceleration of gravity.

The figure in this problem represents the position of the pendulum. We observe that the time it takes for the pendulum to do one complete oscillation is 2.5 seconds.

The time it takes for the pendulum to swing from its position furthest to the right to its position furthest to the left is half the period: therefore, it is

$\frac{T}{2}=\frac{2.5}{2}=1.25 s$

Learn more about period:

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