Question

a damped oscillator of mass 1g has a force constant 10N/m and relaxation time 0.5sec.calculate the angular frequency without damping and with damping. Also find the Q Factor. ​

Answer 1

Explanation:

When the motion of an oscillator reduces due to an external force, the oscillator and its motion are damped. These periodic motions of gradually decreasing amplitude are damped simple harmonic motion. An example of a damped simple harmonic motion is a simple pendulum.

In the damped simple harmonic motion, the energy of the oscillator dissipates continuously. But for a small damping, the oscillations remain approximately periodic. The forces which dissipate the energy are generally frictional

Answer 2

Answer:Angular frequency without damping=100rad/s

Angular frequency with damping=99.99rad/s

Q Factor=50

Explanation: m=1g=10^-3kg

                      c=10N/m

                      τ=.5s

                      τ=1/2k

                      k=1/2τ=1/(2x.5)=1 s^-1

without damping,(ω0) ^2=c/m = 10/10^-3=10^4

                               ω0 = 10^2=100rad/s

with damping,ω=√w0^2-k^2=√10^4-1^2=99.99rad/s

Q Factor=ω0xτ=100x.5=50