The angular frequency of damepd harmonic motion = k m - (b 2 m )^… - Vidyadip

Question

The angular frequency of damepd harmonic motion $\omega=\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}$ where $b$ is called the damping constant. Such the displacement in motion is $x =A e ^{\frac{- bt }{2 m}} \cos (\omega t +\phi)$ and retarding force $F =- b v$ where $v$ is the speed of particle. What can you say from the given equations? Can guess :
(a) How does the oscillation amplitude change?
(b) Does the period of oscillation also change with displacement?

✓

Answer

(a) Oscillation amplitude decreases due to damping force as it is clear from the displacement equation that the oscillation amplitude decreases exponentially. Since damping force depends on velocity.
(b) The period of oscillation does not change in damped oscillation

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