Ablock with mass m =6.7 kg is hung from a vertical spring. when the mass hangs in equilibrium, the spring stretches x = 0.28 m. while at this equilibrium position, the mass is then given an initial push downward at v = 4.6 m/s.
the block oscillates on the spring without friction.1) what is the spring constant of the spring? answer = (234.5)2) what is the oscillation frequency? answer = (0.942)3) after t = 0.47 s what is the speed of the block? 4) what is the magnitude of the maximum acceleration of the block? 5)at t = 0.47 s what is the magnitude of the net force on the block? 6)where is the potential energy of the system the the highest point of the the new equilibrium position of the the lowest point of the oscillation

1)  k = 234.5 N / m, 2)   f = 0.9416 Hz, 3)  v = 4.3 m / s , 4) a = 27.21 m / s² , 5)  182 N, 6)  maximum at the highest point

Explanation:

This is a problem of oscillatory movement  by

         x = A cos (wt + φ )

1) we can use Hooke's law to find the spring constant

        F = k x

        k = F / x

        k = mg / x

        k = 6.7 9.8 / 0.28

        k = 234.5 N / m

2) The angular velocity is

        w = √ k / m

        w = √ 234.5 / 6.7

        w = 5.916 rad / s

Angular velocity and frequency are related.

       w = 2π f

        f = w / 2π

        f = 5.916 / 2π

        f = 0.9416 Hz

3) let's look for the terms of the oscillation equation

For t = 0 v = 4.6 m / s

Speed definition

         v = dx / dt = - Aw sin (wt + φ)

We replace

        4.6 = -A 5.916 sin  (0 + φ)

By this time the body is in the equilibrium position

        0 = A cos (0 + φ)

For this relationship to be fulfilled cos (φ) = 0 ,  the cosine function is zero for φ = π/2

With this value we can find the breadth

          4.6 = -A 5.916 sin (0 + π / 2)

          A = 4.6 / 5.916

           A = 0.7776 m

Now we can write the equation of motion

         x = 0.7776 cos (5.916t + pi / 2)

Let's develop the double angle

         cos (a + 90) = cos a cos 90 - sin 90 sin a = - sin a

With this result the equation is

         x = -A sin wt

         x = - 0.7776 sin (5.916t)

Speed is

         v = -Aw cos wt

          v = - 0.7776 5.916 cos (5.916t)

          v = - 4.6 cos (5,916t)

Let's evaluate for time t = 0.47 s, remember that the angles are in radians

           v = - 4.6 cos (5,916 0.47)

          v = 4.3 m / s

4) the acceleration is

          a = dv / dt

          a = -4.6 5.916 (- sin 5.916t)

          a = 27.2136 sin (5.916t)

The acceleration is maximum when the sine function is worth 1

          a = 27.21 m / s²

5) let's use Newton's second law

         F = m a

         F = 6.7 27.21

         F = 182.3 N

6) Mechanical energy has the formula U = mgh

In general the reference system is taken at the equilibrium point, therefore the power energy is maximum at the highest point

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

happy to

pls mark as brainliest

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.