Question

3) An oscillator with frequency ω knot oscillating in a medium that offers a resistance with
damping coefficient beta. The time period T of damped motion is given by_______?​

Answer 1

An oscillator with frequency ω knot oscillating in a medium that offers a resistance withdamping coefficient beta. The time period T of damped motion is given by

$\boxed{ \bf \: T = \dfrac{2\pi}{ \sqrt{ {( \omega_{0}) }^{2} - { \beta }^{2} } } }$

You need not learn the derivations, instead you can guess the formula using simple logical reasoning.

• Whenever an object is oscillating in a medium providing damping force , it is quite obvious that the time period for the oscillation is going to increase.

• Now, in the denominator we need to subtract the damping coefficient such that the denominator decreases and the whole fraction increases and the time period increases.

• The actual form of the expression is given in the attached image.

$\star$ Hope It Helps.