Question: The total mechanical energy in a simple harmonic oscillator is given by which of the following?
Options:
1/2 kA^2
1/2 mv^2
kA
mv^2
Correct Answer: 1/2 kA^2
Solution:
Total mechanical energy in SHM is E = 1/2 kA^2, where A is the amplitude.
The total mechanical energy in a simple harmonic oscillator is given by which of
Practice Questions
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
Questions & Step-by-Step Solutions
The total mechanical energy in a simple harmonic oscillator is given by which of the following?
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.
Total Mechanical Energy – The total mechanical energy in a simple harmonic oscillator is the sum of its potential and kinetic energy, which remains constant throughout the motion.
Simple Harmonic Motion (SHM) – A type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position.
Amplitude (A) – The maximum displacement from the equilibrium position in SHM, which influences the total mechanical energy.
Spring Constant (k) – A measure of the stiffness of the spring, which affects the potential energy stored in the spring.
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