All Flashcards
How do you determine acceleration from the position equation x = A cos(ωt + φ)?
- Recognize that a = -ω²x. 2. Substitute the position equation into the acceleration equation: a = -ω² * A cos(ωt + φ).
How do you find the maximum velocity in SHM, given the amplitude (A) and angular frequency (ω)?
- Recall the formula: v_max = Aω. 2. Substitute the values of A and ω into the formula. 3. Calculate the result to find the maximum velocity.
How do you find the maximum acceleration in SHM, given the amplitude (A) and angular frequency (ω)?
- Recall the formula: a_max = Aω². 2. Substitute the values of A and ω into the formula. 3. Calculate the result to find the maximum acceleration.
What is the definition of Amplitude (A)?
The maximum displacement from the equilibrium position.
What is the definition of Frequency (f)?
The number of oscillations per second, measured in Hertz (Hz).
What is the definition of Period (T)?
The time it takes for one complete oscillation.
Define Simple Harmonic Motion (SHM).
Back-and-forth motion around an equilibrium point, characterized by periodic changes in displacement, velocity, and acceleration.
What is displacement in the context of SHM?
The distance of an object from its equilibrium position at a given time.
What are the key differences between displacement and velocity in SHM?
Displacement: Position of the object from equilibrium. Velocity: Rate of change of displacement; has a π/2 phase shift relative to displacement.
What are the key differences between velocity and acceleration in SHM?
Velocity: Rate of change of displacement. Acceleration: Rate of change of velocity; 180° out of phase with displacement.
How do Amplitude and Period differ in SHM?
Amplitude: Maximum displacement from equilibrium. Period: Time for one full oscillation; independent of amplitude in SHM.