If the amplitude of a simple harmonic oscillator is doubled, by what multiplicat

Question

If the amplitude of a simple harmonic oscillator is doubled, by what multiplicative factor does the angular frequency change?

If the amplitude of a simple harmonic oscillator is doubled, by what multiplicative factor does the frequency change?

If the amplitude of a simple harmonic oscillator is doubled, by what multiplicative factor does the period change?
If the amplitude of a simple harmonic oscillator is doubled, by what multiplicative factor does the maximum speed change?
If the amplitude of a simple harmonic oscillator is doubled, by what multiplicative factor does the maximum acceleration change?
If the amplitude of a simple harmonic oscillator is doubled, by what multiplicative factor does the total mechanical energy change?

Explanation / Answer

(1)
Angular frequency of the harmonic oscillator is independent of its amplitude of vibrations. So if the amplitude of a simple harmonic oscillator is doubled, there is no change in its angular frequency. (2) Angular frequency = 2(frequency) So frequency also doesn't change if the amplitude of a simple harmonic oscillator is doubled. (3) Time period T = 1 / (frequency) Hence, time period also doesn't change if the amplitude of a simple harmonic oscillator is doubled. (4) As we know the formula for the max speed is                   vmax = A, here is constant Then vmax A So if the amplitude of a simple harmonic oscillator is doubled then the its max speed also doubled. (5) As we know the formula for max acceleration is                amax = A2, here is constant                amax A So if the amplitude of a simple harmonic oscillator is doubled then the its max acceleration also doubled. (6) Total mechanical energy of oscillator is              E = (1/2)kA2 From this, E A2. Hence, if the amplitude of a simple harmonic oscillator is doubled then the mechanical energy is increased by 4 times. (2) Angular frequency = 2(frequency) So frequency also doesn't change if the amplitude of a simple harmonic oscillator is doubled. (3) Time period T = 1 / (frequency) Hence, time period also doesn't change if the amplitude of a simple harmonic oscillator is doubled. (4) As we know the formula for the max speed is                   vmax = A, here is constant Then vmax A So if the amplitude of a simple harmonic oscillator is doubled then the its max speed also doubled. (5) As we know the formula for max acceleration is                amax = A2, here is constant                amax A So if the amplitude of a simple harmonic oscillator is doubled then the its max acceleration also doubled. (6) Total mechanical energy of oscillator is              E = (1/2)kA2 From this, E A2. Hence, if the amplitude of a simple harmonic oscillator is doubled then the mechanical energy is increased by 4 times. So if the amplitude of a simple harmonic oscillator is doubled then the its max acceleration also doubled. (6) Total mechanical energy of oscillator is              E = (1/2)kA2 From this, E A2. Hence, if the amplitude of a simple harmonic oscillator is doubled then the mechanical energy is increased by 4 times.

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