. A damped harmonic oscillator satisfies the equation x+10x+25x=0
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- Chapter 15, Problem 051 GO In the figure, a stick of length L = 1.9 m oscillates as a physical pendulum. (a) What value of distance x between the stick's center of mass and its pivot point o gives the least period? (b) What is that least period? L/2 (a) Number Units (b) Number Units udy Click if you would like to Show Work for this question: Open Show WorkA spring hangs vertically from a ceiling. The spring constant of the spring is k=15 N/m. A 2kg object has been attached to the spring and the spring has already come to its new equilibrium. Someone pulls the object down by 5cm and releases it at time t = 0s. The spring and object begin to oscillate under simple harmonic motion. Find the total energy of the system, the maximum kinetic energy, the maximum potential energy, and the positions where the maximum energies occur. Answers: 0.01875 J, 0.01875 JA simple harmonic oscillator is made from a spring connected to a mass on a frictionless surface. The oscillations have an amplitude of 15cm and a frequency of 0.25Hz . At which point during its oscillation does the oscillator have the most mechanical energy?
- 7. A spring with a spring constant of 55 N/m² is set up horizontally on a frictionless surface with a 3.5 kg mass attached to the spring. If the mass is stretched 0.125 m from equilibrium and released from rest then determine the following:A simple harmonic oscillator consists of a mass m attached to a spring with spring constant k, with displacement given by x = A sin(wt + ¢) . Which one of the following is NOT true? O The frequency is independent of the amplitude O The potential energy is a maximum when (wt + 4) = 0 The kinetic energy is a maximum when (wt + ¢) = 0 O The restoring force must be proportional to the negative of the displacement O Increasing the mass will decrease the frequencyTwo simple harmonic oscillators H1 and H2 of masses on a spring have masses m1 and m2, spring constants k, and k2, and amplitudes A1 and A2. It is found that the total mechanical energy of H2 equals 4H1. Which one of the following will NOT give this relationship? O mị = m2 ; 4k1 = k2 ; A1 = A2 O 4m1 = m2 ; 4k1 = k2 ; A1 = A2 O mi = m2 ; 2k1 = k2 ; (v2) A1 = A2 O 4m1 = m2 ; ki = k2 ; Aı = A2