Question

A oscillator of mass 8 gm is acted upon by a restoring force of 5 dyne / cm and a damping force of

2 dyne-sec/cm. Find whether the motion is over-damped or oscillatory​

Answer 1

Answer:

For damped oscillation,

(a)T=

ω

2π

T=

m

K

−(

2m

l

)

2

2π

T=

200

80×1000

−(

1000×2×200

40×1000

)

2

2×3.14

T=

400−

100

1

6.28

T=0.314s

(b)F×A

2

If amplitude gets reduced to half the force will reduce to one fourth.

F∝a

a∝ω

2

So ω will become half.

T=

ω

2π

T=2×0.314=0.628s

Explanation:

When the damping constant is small, b<√4mk b < 4 m k , the system oscillates while the amplitude of the motion decays exponentially. This system is said to be underdamped, as in curve (a). Many systems are underdamped, and oscillate while the amplitude decreases exponentially, such as the mass oscillating on a spring.