To solve this problem we will apply the principles of conservation of energy, for which we have to preserve the initial kinetic energy as elastic potential energy at the end of the movement. If said equality is maintained then we can affirm that,
Here,
m = mass
k = Spring constant
x = Displacement
v = Velocity
Rearranging to find the velocity,
Our values are,
Replacing our values we have,
Therefore the velocity is
1) The potential energy is the most at the highest position and the least at the equilibrium position
2) The kinetic energy is the most at the equilibrium position and the least at the highest position
Explanation:
1)
The potential energy of an object is the energy possessed by the object due to its position in a gravitational field; mathematically, it is given by
where
m is the mass of the object
g is the strength of the gravitational field
h is the height of the object relative to the ground
For the pendulum in this problem, m is the mass of the bob, and h is the height of the above relative to the ground. We see from the formula that the potential energy is directly proportional to the height:
This means that:
2)
We can solve this part by applying the law of conservation of energy: in fact, the total mechanical energy of the pendulum (sum of potential and kinetic energy) is constant at any time during the motion,
where KE is the kinetic energy.
From the equation above, we observe that:
Therefore, this implies that:
Learn more about kinetic and potential energy:
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