Edits to “Statement”, “Solution”, “Answer”
en/3.5.29.md
+4 −2
| @@ -1,13 +1,15 @@ | |||
| ### Statement | |||
| − | $3.5.29.$ [Insert the problem statement] | ||
| + | $3.5.29.$ Why is the total motion of the oscillator the sum of free and forced oscillations (when the oscillator's displacement and velocity are linearly dependent on the forcing force)? | ||
| ### Solution | |||
| Mathematically, even though the particular solution (as a result of external forcing) satisfies the equation of motion, it cannot satisfies initial conditions (except in a very specific situation). That is why the general solution must contain the complementary solution (as a result of restoring force) as well. | |||
| Physically, as soon as the external forcing displaces the object from its equilibrium, the restoring force comes into play. That is why the total motion is the sum of free and forced oscillations. | |||
| + | Note: The question is answered without regard to the parenthesized phrase in the problem statement as it does not make sense. | ||
| + | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | See the solution. | ||
| @@ -1,13 +1,15 @@ | |||
| ### Statement | ### Statement | ||
| $3.5.29.$ [Insert the problem statement] | $3.5.29.$ Why is the total motion of the oscillator the sum of free and forced oscillations (when the oscillator's displacement and velocity are linearly dependent on the forcing force)? | ||
| ### Solution | ### Solution | ||
| Mathematically, even though the particular solution (as a result of external forcing) satisfies the equation of motion, it cannot satisfies initial conditions (except in a very specific situation). That is why the general solution must contain the complementary solution (as a result of restoring force) as well. | Mathematically, even though the particular solution (as a result of external forcing) satisfies the equation of motion, it cannot satisfies initial conditions (except in a very specific situation). That is why the general solution must contain the complementary solution (as a result of restoring force) as well. | ||
| Physically, as soon as the external forcing displaces the object from its equilibrium, the restoring force comes into play. That is why the total motion is the sum of free and forced oscillations. | Physically, as soon as the external forcing displaces the object from its equilibrium, the restoring force comes into play. That is why the total motion is the sum of free and forced oscillations. | ||
| Note: The question is answered without regard to the parenthesized phrase in the problem statement as it does not make sense. | |||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | See the solution. | ||