The total mechanical energy in a simple harmonic oscillator is given by which of the following?
Practice Questions
1 question
Q1
The total mechanical energy in a simple harmonic oscillator is given by which of the following?
1/2 kA^2
1/2 mv^2
kA
mv^2
Total mechanical energy in SHM is E = 1/2 kA^2, where A is the amplitude.
Questions & Step-by-step Solutions
1 item
Q
Q: The total mechanical energy in a simple harmonic oscillator is given by which of the following?
Solution: Total mechanical energy in SHM is E = 1/2 kA^2, where A is the amplitude.
Steps: 7
Step 1: Understand what a simple harmonic oscillator (SHO) is. It is a system that moves back and forth in a regular pattern, like a pendulum or a mass on a spring.
Step 2: Know that the total mechanical energy in a SHO is the sum of its potential energy and kinetic energy.
Step 3: Recognize that the potential energy (PE) in a spring is given by the formula PE = 1/2 kx^2, where k is the spring constant and x is the displacement from the equilibrium position.
Step 4: In SHM, the maximum displacement from the equilibrium position is called the amplitude (A). So, when the displacement is maximum, x = A.
Step 5: Substitute A into the potential energy formula: PE = 1/2 kA^2.
Step 6: At the maximum displacement (amplitude), all the energy is potential energy, and the kinetic energy is zero. Therefore, the total mechanical energy (E) is equal to the potential energy at maximum displacement.
Step 7: Conclude that the total mechanical energy in a simple harmonic oscillator is E = 1/2 kA^2.
