2. An underdamped oscillator is released from rest at r=0. In this problem we use the...
1. An ideal (frictionless) simple harmonic oscillator is set into motion by releasing it from rest at X +0.750 m. The oscillator is set into motion once again from x=+0.750 m, except the oscillator now experiences a retarding force that is linear with respect to velocity. As a result, the oscillator does not return to its original starting position, but instead reaches = +0.700 m after one period. a. During the first full oscillation of motion, determine the fraction of...
RLC circuit in series A resistor R is connected in series to an inductor L and a capacitor C, without any external emf sources. (a) Using the fact that the energy stored in both the capacitor and the inductor is being dissipated in the resistor, show that the charge on the capacitor q(t) satisfies the differential equation d^2 q/ dt^2 + Rdq/Ldt + q/LC = 0. This is the equation of a damped oscillator and it has a solution of...
You have been asked to design a circuit, shown below, that will deliver a high-current, slightly underdamped, sinusoidal current pulse to a resistive load when the switch is closed at t = 0. You are given the design requirements and parameters listed in the table: a) What values of L and C are required to meet the specifications? b) Calculate the time of the first current peak. c) Calculate the maximum current delivered by the capacitor? d) Calculate the value...
This scenario is for questions 1-2. A simple harmonic oscillator at the position x = 0 generates a wave on a string. The oscillator moves up and down at a frequency of 40.0 Hz and with an amplitude of 3.00 cm. At time t = 0, the oscillator is passing through the origin and moving down. The string has a linear mass density of 50.0 g/m and is stretched with a tension of 5.00 N. a) Find the angular frequency...
The output from a model for the vibration of the tip of a beam is shown in the following figure. 0.8 0.6 0.4 0.2 -0.2 -0.4 0.6 -0.8 10 time (s) This behaviour can be reduced to an expression for the displacement as a function of time: 2(t) = e-kt cos(2nft), where k = 0.5 s-1 and f = 2 Hz. Calculate the values of t in the interval t = 0 to t = 1 for which the amplitude...
just do question 26 and 30 and show all your work (a) Select R so that 26. For the cincuit of Fig. 943,.40 30u-) m v(0+) 6 V. (b) Compute (2 ms). (c) Determine the settling time of the capacitor voltage. (d) Is the inductor current settling time the same as your answer to part (c)? 27. The current source in Fig. 9.43 is id) = 101(1-1) μ A. (a) Select Ri such that iLO")-2 μΑ. Compute L at t-500...
A rectangular loop of wire with dimensions and w is released from rest at time t = 0 from a region with zero magnetic field into a region with uniform magnetic field Bo pointing into the page. At t=0, the upper edge of the loop is in the zero field region and the lower edge is in the uniform field region as shown in the figure below. The loop has mass m and the acceleration due to gravity is g...
Consider the following initial value problem, representing the response of a damped oscillator subject to the discontinuous applied force f(t): y" +2y +10y = f(t), y(0) = 6, 7(0) = -3, f(t) = (1 3<t<4, 10 otherwise. {o In the following parts, use h(t -c) for the Heaviside function he(t) when necessary. a. First, compute the Laplace transform of f(t). L{f(t)}(s) = b. Next, take the Laplace transform of the left-hand-side of the differential equation, set it equal to your...
Assume that we have three independent observations: where Xi ~ Binomial(n 7,p) for i E { 1.2.3). The value of p E (0, 1) is not known. When we have observations like this from different, independent ran- dom variables, we can find joint probabilities by multiplying together th ndividual probabilities. For example This should remind you the discussion on statistical independence of random variables that can be found in the course book (see page 22) Answer the following questions a...
All parts and working needed. Tutorial: Oscillations Block released from rest here IV. More practice wth oscillatory motion A block is connected to a spring, one end of which is attached to a wall. (Neglect the mass of the spring, and assume the surface is frictionless.) The block is moved 0.5 m to the right of equilibrium and released from rest at instant 1. The strobe diagram at right shows the subsequent motion of the block (i.e., the block is...