Answered: Part A: Show that x = A0 exp[-γt/2m]…

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Part A: Show that x = A0 exp[-γt/2m] cos(ωt +φ) is a solution for a damped oscillation. Determine the ω in terms o

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Problem 2: A 200 g oscillator is oscillating at 2.0 Hz in a vacuum chamber. When air is admitted, the amplitude drops 60% in 50 s. How many oscillations will have been completed when the amplitude is 30% of its initial value?
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A mass m=720.0 g and spring with spring constant k oscillates with angular frequency ω=9.80 rad/s and amplitude xm=15.0 cm as in Figure 5. It is maximally stretched at time t=0 (i.e. x(0)=+xm and Φ=0). A. The position as a function of time is x(t) = xm cos(ωt +Φ). Write an expression for v(t). B. Calculate the maximum velocity (i.e the amplitude of the velocity). At what position(s) does themass reach its maximum velocity? Explain. C. Calculate the total mechanical energy E at time t=3 s. D. At t=5s the total mechanical energy E____E at t=3 s. a) > b) = c) < E. Calculate the length L of a Simple Pendulum with the same period T of this mass.
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H In a damped oscillator, let m = 250 g, k=85 N/m, and b=0.070 kg/s. In how many periods of oscillation the mechanical energy of the oscillator drop to one-half of its initial value?
8. A weight of 0.5kg stretches a spring by 0.49m. The spring-mass system is submerged in delicious melted butter with a damping coefficient of y=4. The spring is then lowered by an additional 1.0m and released with velocity 0. There is no external force. Find the function which gives the location of the weight at time t. Note: I have designed this to work out nicely. If it's not working out nicely then you probably got some butter in your calculations.
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Please help.
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