The 5-kg collar has a velocity of 3 m/s to the right when it is at A. It then travels down along the smooth guide shown in (Figure 1). The spring has an unstretched length of 100 mm and B is located just before the end of the curved portion of the rod.
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- Velocity and Acceleration of Simple Pendulum. L= 1m,T0 = 0, θ = 0, θ’ = 10deg/s, θ’’ = 2deg/s*s. Tf = 1sec, θ = 45 deg, θ’ = 5deg/s, θ’’ = 1 deg/s*s Find the position at T0 and TfA uniform disk of radius R = 0.3 meters and mass M = 0.8 kg can oscillate in the vertical plane, around an axis that passes through the pin, indicated in the figure, which is located at a distance “d” from the center of the disk. What is the value of “d” so that the period of oscillation is minimum?Solve the sub-part (B) only, only typing
- Calculate the angular frequency ω (in rad/s) with these numbers: k = 5100 N/m = 5100 kg/s2 m1 = 30 kg m2 = 25 kgGrandfather clocks keep time by advancing the hands a set amount per oscillation of the pendulum. Therefore, the pendulum needs to have a very accurate period for the clock to keep time accurately. As a fine adjustment of the pendulum’s period, many grandfather clocks have an adjustment nut on a bolt at the bottom of the pendulum disk. Screwing this nut inward or outward changes the mass distribution of the pendulum by moving the pendulum disk closer to or farther from the axis of rotation at O. Let mp = 0.7 kg and r = 0.1 m Model the pendulum as a uniform disk of radius r and mass mp at the end of a rod of negligible mass and length L – r, and assume that the oscillations of θ are small. If the pendulum disk is initially at a distance L = 0.85 m from the pin at O, how much would the period of the pendulum change if the adjustment nut with a lead of 0.5 mm was rotated four complete rotations closer to the disk? In addition, how much time would the clock gain or lose in a 24 h…An airplane engine and the pylon that attaches it to the wing are idealized as shown below. Drive the equation of motion for small oscillations. Neglect damping and assume free vibration. The rotational spring shown exerts a restoring moment on the pylon (beam ) which is proportional to the angle the pylon makes with the vertical. The engine has a mass moment of inertia lo about an axis through its mass center. Assume that the pylon(beam) is rigid and weightless. Solve this problem in terms of: - lo, mass moment of inertia of the engine about its own centroid - W, weight of the engine - K, rotational spring constant - L, length of the pylon
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- You have a metal spring of negligible mass that has spring constant k. The spring is supporting an object of mass m which is oscillating up and down with an angular frequency of w. What happens when a large steady current passes through the spring? O The oscillations gradually slow down until they come to a complete stop O The mass continues to oscillate with a reduced oscillation period O The mass continues to oscillate with an increased oscillation period O The mass continues to oscillate with the same oscillation periodIn the arrangement shown in the figure below, an object of mass m = 2.0 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L = 2.0 m. (Ignore the mass of the vertical section of the cord.) The left end of a horizontal cord of density ? is connected to a vibrator at point P. A distance L from point P, the cord goes over a pulley and hangs down. A block of mass m connects to the hanging end of the cord. The vibrator causes the portion of cord between point P and the pulley to oscillate such that standing waves are generated. (a) When the vibrator is set to a frequency of 130 Hz, a standing wave with six loops is formed. What must be the linear mass density of the cord? kg/m(b) How many loops (if any) will result if m is changed to 72.0 kg? (Enter 0 if no loops form.) loops(c) How many loops (if any) will result if m is changed to 14 kg? (Enter 0 if no loops form.) loopsA complicated shape is made to swing about a point that is 192 cm from the center of mass of the object. The mass of the object is 8.23 kg. The time for 30 oscillations was determined to be 99.0 seconds. What is the mass moment of inertia for the object about the center of mass? (Enter your answer to 2 decimal places of kg·m2 and use g = 9.8 m/s2.