To solve this problem, apply the concepts related to Hooke's law. From there we will find the spring constant. Subsequently, applying Energy balance, which includes gravitational potential energy, elastic potential energy and kinetic energy, we will bury the system's energy. Finally, using the displacement expression for the simple harmonic movement, we will find the expression that describes the system.
PART A) The expression for the spring force is

Here,
k = Spring constant
x = Displacement
Rearranging to find the spring constant we have that



PART B ) The gravitational potential energy acts on the spring holds the cart is zero. Since cart is placed in the equilibrium position. The kinetic energy of the cart is zero. Therefore the expression for the total energy is,




PART C) The expression for the angular frequency is



The equation for the motion of the cart is

Replacing,

They did not affect Florida- never came that far South.
Answer:
D
Explanation:
A) is not correct, because the gravitation potential energy will depend on the height the block is located at. It will be calculated with the formula:
U=mgh.
If we take the ground as a zero height reference, then on point 2 the potential energy will be:


While on point 3, the potential energy will be greater.


B) is not the right answer because the kinetic energy will vary with the height the block is located at in the fact that the energy is conserved (this is if we don't take friction into account or air resistance) so in this case:

We already know the potential energy at point 2. We can calculate the kinetic energy at point 3 like this:



So the kinetic energy at point 2 is given by the equation:

so:


As you may see the kinetic energy at point 2 is greater than the kinetic energy at point 3.
C) Is not correct because according to the first law of thermodinamics, energy is not lost, only transformed. So, since we are not taking into account friction or any other kind of loss, then we can say that the amount of mechanical energy at point 1 is exactly the same as the mechanical energy at point 3.
D) Because of what we talked about on part C, this will be the true situation, because the mechanical energy of the block will be the same no matter theh point you measure it at.
To solve this problem, we must basically count the total energy lost converting all the values given in the international system.
The energy loss is given by both 124KJ and 124food heats.
Since the energy conversion we know that 1 food calories is equal to 4,184J. So:

Therefore the total energy lost will be


Therefore the total energy lost to the surroindings in form of heat is 124.518kJ