A 300-g object attached to the end of a spring oscillates with an amplitude of 7.0 cm and a frequency of 1.80 Hz. (a) Find its maximum speed and maximum acceleration. (b) What is its speed when it is 3.0 cm from its equilibrium position

a) v = 0.79 m / s,  a = 8.95 m / s², b)     v = -0.3285 m / s

Explanation:

A simple harmonic motion is described by the expression

        x = A cos (wt + Ф)

the range of motion is A = 7.0 cm = 0.070 m

angular velocity and frequency are related

         w = 2πf

         w = 2π 1.80

         w = 11.3 rad / s

we substitute

        x = 0.070 cos (11.3t +Ф)

a) to find the velocity we use

       v = dx / dt

        v = - Aw sin (wt + Ф)

the maximum velocity when the cosine argument is π/2 0 3π/2 therefore the sine function is ±1

         v = A w

         v = 0.070 11.3

         v = 0.79 m / s

the acceleration is

         a = dv / dt

         a = - A w² cos (wt + Ф)

the acceleration is maximum for an angle of o or pi, consequently the cosine works worth ±1

         a = A w²

         a = 0.070 11.3²

         a = 8.95 m / s²

b) Let's find the time it takes to get to x = 0.03 m

        wt + Ф = x / A

         wt + Ф = 0.03 / 0.07 = 0.42857

To find the value of fi the initial conditions are used, in general if the system is released from rest fi = 0

          t = 0.42857 / w

          t = 0.42857 / 11.3

          t = 0.0379 s

the speed for this time is

          v = -A w sin wt

           v = - 0.07 11.3 sin (11.3  0.0379)

remember angles are in radians

           v = -0.3285 m / s

i believe your answer is d mgf2

answer: d. a cme increases the amount of energy in the solar wind

explanation:

coronal mass ejections, also called cmes, are large clouds of plasma and magnetic field that erupt from the sun. only when the cloud is aimed at earth will the cme hit earth and therefore cause impacts. high-speed solar wind streams come from areas on the sun known as coronal holes.