We don't know what kind of graph it is.
For example, it might be a graph of the pendulum's distance from center,
angle from center, speed, acceleration, total distance swung since it was
started, mass, weight, temperature, etc.
If the graph shows the pendulum's distance from center, angle from center,
speed, or acceleration, then the graph will look like a wave, with the period
of the wave being the period of the pendulum's oscillation. If the pendulum
took longer to complete one oscillation, that means its PERIOD increased,
and the distance between the peaks of the graph would be longer.
If it was a graph of total distance the pendulum swung since it was started,
the graph wouldn't look like a wave, just a steadily rising wiggle line. If the
pendulum took longer to complete one oscillation, the wiggles in the line
would be farther apart, and the average slope of any large section of the
line would be less.
If it was a graph of the pendulum's mass, weight, temperature, cost, etc.,
then the graph would be a horizontal line, and nothing that might change
the period of oscillation would have any effect on the graph.
The distance between peaks would be longer, If the pendulum took longer to complete an oscillation. Option C is correct.
Period:
It is the time taken by the pendulum to complete one oscillation. It is given by the equation,
[tex]\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}}}[/tex]
Where,
[tex]T[/tex] = period
[tex]L[/tex] = pendulum length
[tex]g[/tex] = acceleration due to gravity
Assume the graph is showing the relation between period and distance,
If the pendulum took longer to complete an oscillation, the period will increase.
Therefore, the distance between peaks would be longer, If the pendulum took longer to complete an oscillation.
Learn more about Pendulum:
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