79A linearly damped oscillator has a Q factor of 20. (a) By Equation 14-40 to find...
(1) A damped oscillator has a quality factor of 20. Part A:- By what fraction does the energy decrease during each cycle? Part B:- By what percentage does the damped angular frequency ωd differ from the undamped angular frequency?
Problem 15. (20 pts) Consider a damped driven oscillator with the following parameters s-100 N/m b=0.5kg/s m= 1 kg Fo=2N A) Find the resonant frequency, w. B) Find the damping rate y C) What is the quality factor Q for this oscillator? D) Is this oscillator lightly damped, critically damped, or heavily damped? E) Find the steady state amplitude when the oscillator is driven on resonance (Ω=w). F) Find the steady state amplitude when Ω_w+γ/2. G) Find the average power...
Q.3 Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.
6. The energy levels of a harmonic oscillator with angular frequency w are given by 2 (a) Suppose that a system of N almost independent oscillators has total energy E^Nhw 2 Mhw. Show that the number of states with exactly this energy equals the number of ways of distributing M identical objects among N compartments and that this number 1S MI(N 1) Hint: Consider the number of distinct arrangements of a set of M objects and N -1 partitions (b)...
#18 the last word is uncertainty and the equation is q=e^x #20 The scentence reads: "The equivalent capcitance of this combination_____________" 18. Suppose you measure x to be (3.0 ± 0.1) and then calculate q"e". What is q with its uncertain (a) C0.086 t 0.001) b) (20.086 0.005) (d) (20s 2) (e) None of the above 19. GivenI (12.4 0.3) amps, how precisely do you need to determine the resistance of a roughly 100 ohm resistor so that the error...
April 13, 2020 MATH2107- MIDTERM EXAM.I/1 Q.1(40 pts) Find the solutions of the following differential equa- tion W (2xy + 3y?)dx - (2xy + x2)dy = 0. Q.2(60 pts) Given the differential equation (2xy + y)dx + (2y3 – x)dy = 0. (a) Assuming the integration factor of the form u= u(y), de- termine p(y) so as to make the above equation exact. (b) Then, find the solution of the differential equation. Duration of the exam is 40 minutes.
problem 5 l lbout 0 for a general solution to the given differential equation u, y(0) = 0, V,(0) = 1 . Your answer should include a grneral formula for the ncients. (Find a recursive relation. If possible find Vi and 1,2). 3: Chebyshev's equation i(y + p'y-0, where p is a constant. Find two linearly Independert series solutions yi and ya. (Hint: find the series solution to the differential equation at z-0 to factor ao and ai as we...
(1 point) 14 8 A If AC has length 8 and BC has length 14, find: • The length of AB: • The measure of angle B (in degrees): • The measure of angle C (in degrees): If you use a calculator to find a decimal approximation, your answer must be accurate to at least 3 decimal places. If you're using a calculator, be sure that your calculator is set to degrees, not radians. You are also allowed to use...
1. (30pt) LC Circuit and Simple Harmonic Oscillator (From $23.12 RLC Series AC Circuits) Let us first consider a point mass m > 0 with a spring k> 0 (see Figure 23.52). This system is sometimes called a simple harmonic oscillator. The equation of motion (EMI) is given by ma= -kr (1) where the acceleration a is given by the second derivative of the coordinate r with respect to time t, namely dr(t) (2) dt de(t) (6) at) (3) dt...
Question 3 [20] 3.1. List one (1) factor that can cause a change in the quantity supplied and three (3) factors that can cause a change in supply. 3.2. Using two basic supply curve graphs, illustrate the difference between a change in the quantity supplied and a change in supply. Tip: Show what happens to price and quantity in each case, 3.3. By referring to price and quantity, describe in detail what the situation of equilibrium reflects on a supply...