Question

It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches. Which function models the horizontal displacement as a function of time in seconds? y = 5 cosine (StartFraction 2 pi Over 3 EndFraction x) y = 5 cosine (StartFraction 4 pi Over 3 EndFraction x) y = 10 cosine (StartFraction 2 pi Over 3 EndFraction x) y = 10 cosine (StartFraction 4 pi Over 3 EndFraction x)

Answer 1

The horizontal displacement of a grandfather clock's pendulum as a function of time can be modeled using the equation y = 10 cosine (\frac{2 \pi}{3} x).

Step-by-step explanation:

The horizontal displacement of a pendulum can be modeled using the equation: y = 10 cosine (\frac{2 \pi}{3} x)

Where:

• y represents the horizontal displacement
• x represents the time in seconds
• 10 represents the amplitude of the displacement
• \frac{2 \pi}{3} represents the angular frequency

The given equation y = 10 cosine (\frac{2 \pi}{3} x) matches the description of the pendulum's displacement over time, covering a distance of 10 inches in 1.5 seconds.

Answer 2

Step-by-step explanation:

Given functions are

y = 5 cos ( 2π / 3 ) t

y = 5 cos ( 4π / 3 ) t

y= 10 cos ( 2π / 3 ) t

y = 10 cos ( 4π / 3 ) t

The pendulum half oscillation from left extreme to right extreme takes 1.5 s

So its time period of oscillation T = 1.5 x 2 = 3 s .

standard equation of oscillation is

y = A cos ω t where A is amplitude and ω is angular frequency .

Amplitude of oscillation A = 10 / 2 = 5 inch .

Among the given equation of motion only first two has amplitude equal to 5 . So both the last two are ruled out .

The angular frequency of first motion as per given equation

ω = 2π / 3

If time period is T

2π / T = 2π / 3

T = 3 s

So it matches with the time period of oscillation of pendulum .

Hence the first equation truly represents the oscillation of pendulum.