Question

John and Jim are on a swing set next to each other. They want to perform a physics experiment on oscillatory motion. John will start his swing 3 degrees back from equilibrium, and Jim will start his swing 9 degrees back from equilibrium. Based on what you know about oscillatory motion, who between John or Jim will reach the equilibrium position first? John and Jim are on a swing set next to each other. They want to perform a physics experiment on oscillatory motion. John will start his swing 3 degrees back from equilibrium, and Jim will start his swing 9 degrees back from equilibrium. Based on what you know about oscillatory motion, who between John or Jim will reach the equilibrium position first? John will reach first because he has less distance to travel. Jim will reach first because he has more energy and therefore more velocity. We can't tell who will reach the bottom first because we need to know their masses, as the gravitational acceleration plays a key role. Both will reach the equilibrium position simultaneously because the frequency doesn't depend on the amplitude.

Answer 1

Take into account that both John and Jim on the swing set, can be considered as independent pendulums.

You have that the period of a pendulum is given by:

`T=2\pi\sqrt[]{(l)/(g)}`

where,

l: length of the pendulum

g: gravitational acceleration constant.

As you can notice, the period of oscillation (and then the frequency) of a pendulum does not depend of the angular amplitud of oscillation. Moreover, take into account that the period of oscillation determines the time each John and Jim take to reach the bottom.

Hence, you can conclude:

Both will reach the equilibrium position simultaneously because the frequency doesn't depend on the amplitude.