- #1
Edel Crine
- 89
- 12
- Homework Statement
- A restoring force of unknown magnitude is exerted on a object
that oscillates with a period of 0.50 s.
When the object is in an evacuated container, the motion is simple harmonic motion, with an amplitude of 0.10 m.
When air is allowed into the container, the amplitude decreases by 2.0% with each cycle of the oscillation.
(a) What is the amplitude after 25 cycles?
(b) What fraction of the initial energy is left 6.3 s after air is admitted?
- Relevant Equations
- A\left(t\right)=A_{0}e^{-\frac{t}{2τ}}
w_{d}=w\sqrt{1-\frac{\frac{b^{2}}{m^{2}}}{4w^{2}}}
My attempts were these,
a) 2.0% / cycle * 25 cycles = 50%
So, I got half of the first amplitude which is 0.5 m (seems not right though...)
b) w=2pi/T , so put 0.5 at T, I got w=12.6 cycle/sec
12.6 cycle / sec * 6.3 sec = 79.2 cycles and it is obviously not right to me...
May I get some help from you all...? Thank you so much...!
a) 2.0% / cycle * 25 cycles = 50%
So, I got half of the first amplitude which is 0.5 m (seems not right though...)
b) w=2pi/T , so put 0.5 at T, I got w=12.6 cycle/sec
12.6 cycle / sec * 6.3 sec = 79.2 cycles and it is obviously not right to me...
May I get some help from you all...? Thank you so much...!