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How are each of the following properties of a simple harmonic oscillators affected by doubling the amplitude; period, force constant, total mechanical energy, maximum velocity, maximum acceleration?

How are each of the following properties of a simple harmonic oscillators affected by doubling the amplitude; period, force constant, total mechanical energy, maximum velocity, maximum acceleration?

Grade:upto college level

1 Answers

Jitender Pal
askIITians Faculty 365 Points
8 years ago
Time period (T) of simple harmonic oscillation is defined as,
T = 2π √m/k
Here, m is the mass of the oscillator and k is the force constant.
From the above equation, T = 2π √m/k we observed that, the time period (T) of simple harmonic oscillation does not depend upon the amplitude of oscillation xm. Therefore the time period (T) of simple harmonic oscillation will not affected if we the doubling the amplitude of the oscillation.
Total mechanical energy (K) of the simple harmonic oscillation is defined as,
K = ½ kxm2
Here, k is the force constant and xm is the amplitude of oscillation.
If we double the amplitude of oscillation xm, then the new mechanical energy (Knew) of the simple harmonic oscillation will be,

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