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Ksivusya [100]
3 years ago
10

Write down the DE of this damped harmonic oscillator.

Physics
1 answer:
ohaa [14]3 years ago
4 0

Answer:

\frac{d^{2}x }{d^{2}t }+\frac{k}{m}x+\frac{b}{m} \frac{dx}{dt}=0

Explanation:

The spring mass equation for the damped oscillation will be,

F=-kx-bv

Here, -bv is the damping term used in this b is damping constant, k is spring constant, x is elongation in the spring, F is the force.

ma=-kx-bv\\m\frac{d^{2}x }{d^{2}t }=-kx-b\frac{dx}{dt}\\  m\frac{d^{2}x }{d^{2}t }+kx+b\frac{dx}{dt}=0\\\frac{d^{2}x }{d^{2}t }+\frac{k}{m}x+\frac{b}{m} \frac{dx}{dt}=0

Therefore the differential equation for the damped harmonic oscillator is,

\frac{d^{2}x }{d^{2}t }+\frac{k}{m}x+\frac{b}{m} \frac{dx}{dt}=0

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