Pendulum Simulation

The graph on the left shows the cosine function curve, while the graph on the right simulates the real-time motion of a pendulum.

Pendulum Motion and the Cosine Function
The motion of a pendulum can be described using the cosine function:
d(t) = A · cos(B t)

A (Amplitude): Maximum distance from the resting position.
B (Frequency Parameter): Determines how fast the pendulum swings.
Period (T): Time for one full swing back and forth: T = 2π / B
Cosine is used because at t=0 the pendulum is at its farthest position, where cos(0)=1.

d(t) = 3·cos(3t)

A (Max Distance): 3 B (Frequency Parameter): 3.14

Pendulum Motion Problem (Multiple Choice)

The motion of a pendulum can be described by the following cosine function:

d(t) = 5 · cos(π t)

Starting from the beginning of its swing (t=0), how long does it take for the pendulum to return to its farthest right position for the first time?

A) 0.5 seconds
B) 1 second
C) 2 seconds
D) 4 seconds

Answer and Explanation

Thought Process:

The pendulum returns to its "farthest right position" after completing one full period (T).

For d(t) = 5 · cos(π t), the frequency parameter B = π.

Period formula: T = 2π / B

Substitute B = π → T = 2π / π = 2 seconds.

Correct answer: C) 2 seconds