If the amplitude of a simple harmonic motion is halved, how does the maximum vel

If the amplitude of a simple harmonic motion is halved, how does the maximum velocity change?

If the amplitude of a simple harmonic motion is halved, how does the maximum velocity change?

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.

Simple Harmonic Motion – The study of oscillatory motion where the restoring force is proportional to the displacement from equilibrium.
Amplitude – The maximum extent of a vibration or oscillation, measured from the position of equilibrium.
Maximum Velocity – The highest speed reached by an object in simple harmonic motion, calculated as V_max = ωA.
Angular Frequency (ω) – A measure of how quickly an object oscillates, related to the period of the motion.