A damped harmonic oscillator has m = 360 g and k = 15 N/m. The initial amplitude of oscillation is observed to be 0.0500 m. After three oscillations the amplitude is 0.00200 m. a) Determine the Q for this system from the information given. b) Determine the damping constant, b (in standard MKS units).
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- Given the function f(x) – - 1 sin(z) a. Equation of midline: b. Amplitude: c. Draw the graph. -2 -72 -1 37/2 27 -2At t=0, the displacement of a point x(0) in a linear oscillator is -8.6 cm, its velocity V(0)= -0.93 m/s and its acceleration a(0)= +48m/s2 . A- What is the angular frequency ω and the frequency f? B- What is the phase constant? C- What is the amplitude of the motion?The pendulum shown below consists of a uniform disk with radius r = 2.35 cm and a mass of 460 grams. The disk is supported in a vertical plane by a pivot located d = 1.75 cm from the center of the disk. Pivot• R. a. What is the frequency of oscillation if the disk is displaced by a small angle and released? Hz b. What is the frequency of oscillation if the mass of the disk is and then displaced by a small angle and released? Hz
- A cart of mass m = 1.6 kg placed on a frictionless horizontal surface and connected to a spring with spring constant 6 N/m. The damping force strength is given by b = 255 g/s. The cart is pulled away 16.5 cm and released. k m 'b a. Calculate the time required for the amplitude of the resulting oscillations to fall to 1/7 of its initial value. 24.4 b. How many oscillations are made by the cart in this time? 7.51A 37 kg block on a horizontal frictionless surface is attached to a spring. The block is exhibiting SHM. The total energy of the system is 420 J. A.) Determine how much PE it has when its KE is six-sevenths of the PE. PE= w B.) Determine the maximum speed of the block. Vmax=A mass m = 3.3 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A = 4.5 cm and a frequency f = 1.5 Hz. a. Write an equation for the spring constant k. b. Calculate the spring constant k, in Newtons per meter. c. Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement. d. Calculate the total mechanical energy E, in joules.
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