If the amplitude of a simple harmonic motion is doubled, how does the maximum velocity change?
Practice Questions
1 question
Q1
If the amplitude of a simple harmonic motion is doubled, how does the maximum velocity change?
It doubles
It quadruples
It remains the same
It halves
Maximum velocity V_max = Aω. If A is doubled, V_max also doubles.
Questions & Step-by-step Solutions
1 item
Q
Q: If the amplitude of a simple harmonic motion is doubled, how does the maximum velocity change?
Solution: Maximum velocity V_max = Aω. If A is doubled, V_max also doubles.
Steps: 6
Step 1: Understand that in simple harmonic motion, the maximum velocity (V_max) is calculated using the formula V_max = Aω, where A is the amplitude and ω is the angular frequency.
Step 2: Recognize that if the amplitude (A) is doubled, it means we replace A with 2A in the formula.
Step 3: Substitute 2A into the formula: V_max = (2A)ω.
Step 4: Notice that this can be rewritten as V_max = 2(Aω).
Step 5: Realize that Aω is the original maximum velocity, so V_max = 2V_max(original).
Step 6: Conclude that if the amplitude is doubled, the maximum velocity also doubles.
