(1 point) Suppose a pendulum of length L meters makes an angle of θ radians with the vertical, as in the figure. It can be shown that as a function of time, θ satisfies the differential equation
d2θdt2+gLsinθ=0,
where g=9.8 m/s2 is the acceleration due to gravity. For θ near zero we can use the linear approximation sin(θ)≈θ to get a linear differential equation
d2θdt2+gLθ=0.
Use the linear differential equation to answer the following questions.

(a) Determine the equation of motion for a pendulum of length 2 meters having initial angle 0.4 radians and initial angular velocity dθdt=0.1 radians per second.

θ(t)=
0.4cos(2.21t)+0.09sin(2.21t)
radians

(b) What is the period of the pendulum? That is, what is the time for one swing back and forth?

Period =
2sqrt10/sqrt49pi
seconds

43

step-by-step explanation:

the answer is 9.8975

explanation:

when you multiply the "39.59" with the 25% it reduces it and shows its final discounted price. hope this !

step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.