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How do you determine acceleration from the position equation x = A cos(ωt + φ)?

  1. Recognize that a = -ω²x. 2. Substitute the position equation into the acceleration equation: a = -ω² * A cos(ωt + φ).

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How do you determine acceleration from the position equation x = A cos(ωt + φ)?
1. 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)?
1. 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)?
1. 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 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.
What is Simple Harmonic Motion (SHM)?
Oscillations that follow a smooth, repeating pattern (sine or cosine wave).
Define Amplitude (A) in SHM.
The maximum displacement of an object from its equilibrium position.
Define Frequency (f) in SHM.
The number of oscillations per unit time.
What is Angular Frequency (ω)?
A measure of the oscillation rate, related to frequency by ω = 2πf.
Define the Phase Constant (φ) in SHM.
Determines the initial position of the oscillating object at time t = 0.
What is Resonance?
The phenomenon where the amplitude of an oscillation increases dramatically when an external force is applied at the system's natural frequency.
What is Natural Frequency?
The frequency at which a system oscillates freely without any external force.
Define Period (T) in SHM.
The time taken for one complete oscillation.