Astronauts in space "weigh" themselves by oscillating on a spring. suppose the position of an oscillating 70 kg astronaut is given by x=(0.34m)sin((πrad/s)⋅t), where t is in s. what force does the spring exert on the astronaut at t = 1.0s. note that the angle of the sine function is in radians.

x = 0 , F= 0

Explanation:

To find the elastic force of a spring we use Hooke's law

      F = - k x

Done k is the Hooke constant and x is the displacement of the spring from its equilibrium point.

They give us the equation of motion of the harmonic oscillator

     x = 0.34 sin (π t)

  The form of the theoretical equation is

     x = A cos (wt + Φ)

To transform the expression the phase must be 90º and the angular velocity is

     w² = k / m

      x = A cos (wt + 90) = A [cos wt sint 90 + cos 90 sint wt]

     Cos 90 = 0

      x = A sin( wt)

Now let's calculate the offset for 1 s

      x = 0.34 sin (π 1)

      x = 0.34 (0)

      x = 0

For this displacement the force is zero

the five characteristics of adolescence are biological growth and development, and undefined status, increased decision making, increased pressure and the search of self.

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)