Final answer:
The question pertains to the calculation of mechanical energy within a simple harmonic oscillator system, which encompasses both potential and kinetic energies. Various points during the oscillation are considered for calculating energy values.
Step-by-step explanation:
The student is asking about the total mechanical energy of a block oscillating horizontally on a spring. This scenario typically involves calculating both kinetic and potential energy at different points of the oscillation, and understanding the conservation of energy within a simple harmonic motion system.
(a) The potential energy stored in the spring at maximum compression can be calculated using the equation Ep = 1/2 k x 2, where k is the spring constant and x is the compression distance.
(b) The speed of the block when crossing the equilibrium point (where the spring is neither compressed nor stretched) can be determined using the conservation of mechanical energy, such that the potential energy stored in the spring is completely converted into kinetic energy (KE = 1/2 m v2).
(c) To find the speed of the block 20 cm from the release point, we again use conservation of energy principles taking into account both the kinetic energy and the potential energy of the spring at that point.
Example Calculation:
For the pendulum question, we know that at the center of oscillation, all the energy of the pendulum is kinetic. Hence, the energy of the pendulum can be found using KE = 1/2 m v2, which gives us 2.5 Joules for a pendulum with a mass of 0.2 kg and a speed of 5 m/s.