Discussing free vibrations and show that the frequency of oscillation for such a system is given by: 1 k 27 m
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- a particle of mass m makes simple harmonic motion with force constant k around the equilibrium position x = 0. Calculate the valu of the amplitude and the phase constant if the initial conditions are x(0) = 0 and v(0) = -Vi (vi > 0). Draw x-t, v - t and a - t figures for one complete cycle of oscillations.A body in simple harmonic motion has a velocity of 8cm/s when its displacement is 2cm and a velocity of 2 cm/s when the displacement is 8 cm. what is the amplitude of the oscillation?While seated on a tall bench, extend your lower leg a small amount and then let it swing freely about your knee joint, with no muscular engagement. It will oscillate as a damped pendulum. as shown is a graph of the lower leg angle versus time in such an experiment. Estimate (a) the period and (b) the timeconstant for this oscillation.
- MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A "seconds pendulum" is one that moves through its equilibrium position once each second. (The period of the pendulum is precisely 2.000 s.) The length of a seconds pendulum is 0.9920 m at Tokyo and 0.9948 m at Cambridge, England. What is the ratio of the free-fall accelerations at these two locations? (g Cambridge / g Tokyo) =A simple harmonic motion of a point mass m can be expressed byx = 0.25sin(4pt +p/6) m ( time t in ses). a)Find the amplitude for the oscillation in m. b)Find the frequency of the oscillation (in Hz). c)Find the maximum speed for the oscillation (in m/s d)Find the maximum acceleration for the oscillation (in m/s2 ) e)Find the initial position of the mass m (in m) f)Find the total energy for the oscillation (in Jules)A protein dimer can be viewed as a dumbbell linked by a spring. Stretching of the spring with an AFM cantilever adds the total (internal) energy of 10−17 J to the dimer. What is the average kinetic energy of dumbbell oscillations after the external force has been released? Help me
- A mathematical pendulum swings with angular amplitude α (α ≪ 1), its period is T . By what factor does the period of the pendulum change if it is suddenly surrounded by two perfectly elastic walls (see figure)? The walls are arranged symmetrically, their angular distance is α.(a) Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.) (b)Write an equation that represents the curve in the form(B) llllllll Students set up an experiment by attaching an ideal vertical spring to a support and hanging a block of known mass from the spring. The students pull the block down and release it from rest. The students then measure the period of the block's oscillation. This procedure is repeated for several trials using the same spring but with blocks of different known masses. The students are instructed to create a linear graph using the mass m of each block and the period T of the block's motion. The slope of the graph will be used to calculate the force constant k of the spring. Which of the following best indicates how the students should create their linear graph and how k can be calculated from the slope of the graph? E k Graph T on the vertical axis and m on the horizontal axis; set k = 2π slope Graph T² on the vertical axis and m on the horizontal axis; set k Graph T on the vertical axis and m² on the horizontal axis; set k Graph T² on the vertical axis and m on the horizontal…
- The frequency of a damped simple harmonic oscillator is given by w? = wở – 4m2 a- If w-w² 10-?wổ. find the value of Q- factor and logarithmic decrements b- If wo = 10-6 and the mass 10-10 kg , find the value of stiffness constantA curious physics student places an object with mass M at the end of a spring, and sets it oscillating. The student then wants to double the period of oscillation by changing the mass. They should replace the mass with:Two particles execute simple harmonic motion with the same amplitude. One particle has twice the frequency of the other. Compare their maximum velocities and accelerations.