SUMMARY
The total energy of a mass-spring oscillator with a mass of 2 kg and a displacement function of x(t) = 2cos(6πt) can be calculated using the formula for maximum speed and kinetic energy. The angular frequency (ω) is determined to be 6π rad/s. The maximum speed (v(max)) is calculated as v(max) = Aω = 2 * 6π = 12π m/s. The total energy (E) is then calculated using the kinetic energy formula KE = 1/2 mv(max)², resulting in a total energy of 144π² J, which approximates to 1420 J, aligning with option B in the provided choices.
PREREQUISITES
- Understanding of simple harmonic motion (SHM)
- Familiarity with kinetic energy calculations
- Knowledge of angular frequency and its relation to oscillators
- Ability to manipulate trigonometric functions in physics equations
NEXT STEPS
- Study the principles of simple harmonic motion in depth
- Learn about the derivation and application of the kinetic energy formula
- Explore the relationship between angular frequency and maximum speed in oscillatory systems
- Practice solving problems involving total energy in oscillators
USEFUL FOR
Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of energy calculations in simple harmonic systems.