Answer:
The equation will be altered by doubling the angular velocity of motion, resulting in d(s) = 7·sin(720s)
Step-by-step explanation:
The current equation of the pendulum-like motion of the pocket watch is d(s) = 7sin(360s)
The formula for simple harmonic motion is x = A·sin(ω₁t + ∅)
By comparing, we find;
x = d(s)
A = 7
ω₁t = 360
∅ = 0
The period of oscillation is the duration needed for a complete cycle, calculated as 2·π/ω₁.
Thus;
ω₁ = 2·π/T₁
When the frequency of the swing doubles, the time taken to complete one cycle is halved, hence, the new period is T₂ = T₁/2.
Consequently, ω₂ = 2·π/T₂ = 2·π/(T₁/2) = 4·π/T₁ = 2ω₁.
The revised equation becomes:
x = A·sin(ω₂t) = A·sin(2ω₁t) leading to;
d(s) = 7·sin(2 × 360s) = 7·sin(720s).
This illustrates the modification due to an increase in the angular frequency of motion.
The likelihood that John scores on the first attempt and misses the second is:
Step-by-step explanation:
The difference quotient represents the slope of the line connecting two points on a curve. To achieve the most accurate estimate, we need to use points that are nearest to x = 0. For this problem, the relevant points are (-0.001, 1.999) and (0.001, 2.001).
m = (2.001 − 1.999) / (0.001 − (-0.001))
m = 1
There are 50 pairs of whole numbers that can add up to 99. To clarify, consider the combinations: 0 + 99, 1 + 98, 2 + 97, and so on, up to 49 + 50. This observation indicates that counting all combinations would result in 50 pairs of distinct whole numbers that sum to 99. I hope this response assists you!
