The period is 2*pi/w where w=sqrt(K/m).

The amplitude is determined by the kinetic energy after the collision by .5KA^2= .5mv^2, so A=v* sqrt(m/K).

To find the velocity, use conservation of momentum for the inelastic collision of the bullet and the block.

First, use Newtons second law with the force of friction to find the acceleration. Then use the kinematic equation v^2=vo^2+2ad to find the velocity of the cars after the crash. This velocity is v_f of a collision problem. It's a simple conservation of momentum to solve for the velocity of the Maserati.

It will rotate about it's center of mass. It will have transverse motion since it has linear momentum

The percent submerged is

%=density_object/density_fluid.

You can find the density of the object by m/V, and the density of the fluid is (specific gravit)×(density if water, 1000 kg/m^3)

Recall that the force on a charged particle in a magnetic field it F=qvxB. This is always perpendicular to the velocity. Remember from circular motion that forces perpendicular to the velocity never causes changes in speed, only direction.

the local gravitational constant g is the gravitational acceleration. It is found by

g =GM/r^2. At the surface of earth, it's value is 9.81 m/s/s. At twice the radius of earth, you can see that it should be 1/4 the acceleration, so 2.45 m/s/s

The more formal Newtons second law is

F=dp/dt. With constant mass, this is m(dv/dt), but if mass is changing, it is

m(dv/dt)+ (dm/dt)v.

This problem could be evaluated the following 2 methods: energy conservation or balancing forces.

(1/2)*kx^2 = (1/2)*mv^2

or

kx = ma

Then, you solve the equation for either v or the second order equation depending the approach you choose.

Afterwards, you should simply find the distance that is necessary to go past that length l that you choose for x.

The answer is no for the following reason, there would be a force the instant he throws one of the balls into the air. This would be pushing the juggler downward adding onto the weight that he has in his hands.

The reason the forces are balanced initially (before having the child move closer) is because the mass of one child caused an upward force on the other side. On the other hand, when one of them comes closer it causes an imbalance to happen because one of the child is closer. Thus, the answer to your question is no. The sum of the forces does not remain zero.