Physics Problem ☺ ☻ ☺?

Question

A 0.3 kg block attached to a spring of force constant 10.8 N/m oscillates with an amplitude of 17 cm.

1) Find the maximum speed of the block in m/s

2) Find the speed of the block when it is 8.5 cm from the equilibrum position in units of m/s.

3) FInd its acceleartion at 8.5 cm from the equilibrium position in units of m/s^2.

4) Find the time it takes the block to move from x=0 to x=8.5 cm in units of s.

Answer 1

This isn't very hard - you just need to do each of the little pieces. I'll give some hints.
1) When the block is at the extreme from the rest position all the system energy is stored in the spring. The stored energy is spring force (k*x) times spring deflection distance (x). So it's k*x^2 where x is 8.5.

The block has maximum speed when the block is in the center of the oscillation range (the spring is fully relaxed at that point), so all the energy is in kinetic energy. Energy is conserved, so
Max spring energy = Max KE
k*x^2 = (1/2)*m*v^2

2) Best hint here: think, no math req'd.

3) Spring force F = k*x. Acceleration = F/m

4) Acceleration is max (see #3) at x = 8.5 and zero at x = 0. In the formula
x = (1/2)*a*t^2,
you can use the average of the accelerations those 2 points for a.

Answer 2

the galaxies rotate at speeds inconsistent with their obvious mass is via the fact we do see all of it. i'm bearing on it as being the theoretical dark count. There are very good proofs that shows that dark count exist. One the is the inconsistent speed of and obvious mass. dark count makes up approximately seventy 5% to 80% of the situation interior the Universe...