If the amplitude of a simple harmonic motion is halved, how does the maximum velocity change?
Practice Questions
1 question
Q1
If the amplitude of a simple harmonic motion is halved, how does the maximum velocity change?
Halved
Doubled
Remains the same
Quadrupled
Maximum velocity V_max = ωA. If A is halved, V_max is also halved.
Questions & Step-by-step Solutions
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Q
Q: If the amplitude of a simple harmonic motion is halved, how does the maximum velocity change?
Solution: Maximum velocity V_max = ωA. If A is halved, V_max is also halved.
Steps: 6
Step 1: Understand that in simple harmonic motion, the maximum velocity (V_max) is calculated using the formula V_max = ωA, where ω is the angular frequency and A is the amplitude.
Step 2: Recognize that amplitude (A) is the maximum distance from the equilibrium position in the motion.
Step 3: If the amplitude (A) is halved, it means we change A to A/2.
Step 4: Substitute the new amplitude into the formula: V_max = ω(A/2).
Step 5: Simplify the equation: V_max = (ωA)/2, which shows that the new maximum velocity is half of the original maximum velocity.
Step 6: Conclude that if the amplitude is halved, the maximum velocity is also halved.
