An irregularly shaped flat object of mass 2.00 kg is suspended from a point at a distance d from its center of mass and allowed to undergo simple harmonic motion in the vertical plane. the object has moment of inertia i = 1.28 kg · m2 about an axis passing through the point of suspension and perpendicular to the plane of the object. the frequency of this oscillatory motion is 0.660 hz. what is the distance d of the pivot point from the center of mass of the object?

1.12191 m

Explanation:

m = Mass of point = 2 kg

f = Frequency = 0.66 Hz

I = Moment of inertia = 1.28 kgm²

g = Acceleration due to gravity = 9.81 m/s²

For a compound pendulum the angular velocity is given by

The distance of the pivot point from the center of mass of the object is 1.12191 m

this is poiselle's equation from fluid mechanic in physics. mech eng

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.