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What changes could you make in a harmonic oscillator that would double the maximum speed of the oscillating object?
Kinetic energy in simple harmonic motion is the energy possessed by the particle by virtue of its motion.The maximum kinetic energy in simple harmonic motion is defined as,(K) max = ½ mw2r2 …… (1)Where m is the mass of the body, w is the angular frequency of the oscillation and r is the amplitude of the oscillation.But kinetic energy K is defined as,K = ½ mv2 …... (2)Where m is the mass of the body and v is the velocity of the body.Substitute equation (2) in equation (1),½ mv2 = ½ mw2r2So, v = wr …… (3)From equation (3) we observed that, since mass (m) is not the fundamental property of the pendulum, therefore keeping mass as a constant quantity, you have to double either frequency of the previous angular frequency of oscillation w or amplitude of the oscillation r to double the maximum speed of the oscillating object.
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