Question

A student does an experiment with a pendulum. In the first trial, she displaces the pendulum 5 cm. In the second trial, she displaces the same pendulum a distance of 10 cm.
In what ways would the graphs that represent these simple harmonic motion graphs be different? In what ways would they be the same?

Answer 1

The displacement of the pendulum is directly proportional to the amplitude of the sine wave produced. The period would not change because the length of the pendulum rod remains the same.

Answer 2

Answer:

The graphs that represent the displacement would be different, while the graphs that represent the period would be the same

Explanation:

The displacement of the two pendulums is different. In fact, in the first trial the amplitude of the oscillation of the pendulum is 5 cm, while in the second trial the amplitude of the oscillation is 10 cm. Since the displacement is given by the equation

$x(t)=A sin(\omega t)$

where A is the amplitude, we see that the displacement x(t) of the two trials will be different.

On the contrary, the period of oscillation in the two trials will be the same. In fact, the period of a pendulum is given by

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

where L is the length of the pendulum and g is the acceleration due to gravity. we see that the period depends only on the length of the pendulum, L, so since the same pendulum is used in the two trials, we can conclude that the period will be the same.