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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 is the effect of applying an external force at the natural frequency of a system?
Resonance occurs, leading to a dramatic increase in the amplitude of oscillation.
What is the effect of increasing the spring constant (k) on the period of oscillation?
The period of oscillation decreases.
What is the effect of increasing the mass (m) on the period of oscillation?
The period of oscillation increases.
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.