Question

A metal block with a mass of 8.80 kg oscillates at the end of a vertical spring with a spring constant of 2.20 x 104 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N. s/m. (a) What is the frequency (in Hz) of the damped oscillation? THz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? % c) Over what time interval (in s) does the energy of the system drop to 4.00% of its initial value? s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in (d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is represented by b = 150 N the atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? Hz What is the percentage decrease in amplitude in each cycle? What is the time interval (in s) for the energy to drop to 4.00% of its initial value?

Answer 1

1) Frequency if undamped would be I (0o= (k = 2. 20x10 N/m J 8.80 kg = 50/5. a) with damping W = 60 - (im) = 50 $ face - So =) 7.96 Hz

w ) r a= to e-bt/2m cos (@t+9) oven one cycle, a teme J = 211, the amplitude changes brom Ao to A - 627/2mce bo a fractional decrease of Ao - Ao e Tib/mas - 11139/18 50x450) - = 1-1 Ao 1-e0014 = l-e-0.0214 31-01978 = 0.022 =) The energy is proportional to 12 2 1 uare of the amplitude, so its fractional rate of decrease is turize as fast: 26t/2m , & -bthm E-KA - KAė 0.04E05 toe - 3+/8.80 kg. =) 0:04-034 y = 3.91 t = 91415 tol -3+/8.80
According to the guideliness i did first question completely..