A mass-on-a-spring system has a spring constant k = 384 N/m and a mass m = 0.51 kg.
(a) If it is given an initial displacement of 0.22 m and then released, what is the initial potential energy of the oscillator? = 9.29 J
(b) What is the maximum kinetic energy of the oscillator? ____ J
I need help with part B, please explain!
After release, there is no more energy input, so the sum of potential and kinetic energies
= constant
=9.29 J
At the equilibrium position, the potential energy is zero, so the kinetic energy is at its maximum and equal to ______ J.
To find the maximum kinetic energy of the oscillator, we need to use the concept of conservation of energy. In a mass-on-a-spring system, the total mechanical energy (E) remains constant over time, which means the sum of kinetic energy (KE) and potential energy (PE) remains constant.
The equation for total mechanical energy is:
E = KE + PE
In part (a) of the question, we found the initial potential energy of the oscillator to be 9.29 J. Since the system is released from rest at the initial displacement, the initial kinetic energy is zero (KE = 0).
Therefore, at the maximum displacement (when the potential energy is zero), all the initial potential energy (9.29 J) is converted into kinetic energy.
So, the maximum kinetic energy of the oscillator is 9.29 J.
To summarize:
(a) Initial potential energy = 9.29 J
(b) Maximum kinetic energy = 9.29 J