There are three identical rods and each of the has a mass of 1 kg and length of 39.2 cm. They are used in constructing a rigid body as seen in the figure. What is the period of small oscillations if it was pivoted at an axis through P? Take note that the center of mass of the rigid body is at Q. L L/2 P L/2
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- A peg on a turntable moves with a constant tangential speed of 0.67 m/s in a circle of radius 0.26m. The peg casts a shadow on a wall. Find the following quantities related to the motion of the shadow.1) Find the period. Express your answer using two significant figures. T=(?)s2) Find the amplitude. A=(?)m3) Find the Max Speed Vmax= (?) m/s4) Find the maximum magnitude of the acceleration. aMax=(?)m/s^2An object is attached to a coiled spring. The object begins at its rest position at t = 0 seconds. It is then propelled downward. Write an equation for the distance of the object from its rest position after t seconds, if the amplitude is 7 inches and the period is 5 seconds The equation for the distance d of the object from its resting position isMM12.. no handwritten...
- a) Use energy conservation to find the amplitude of the motion. b) Use energy conservation to find the maximum speed of the glider. c) What is the angular frequency of the oscillations? (express in rad/s)A 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?Grandfather 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…
- A simple pendulum consists of a bob of mass of 0.85 kg attached to a string of length 1.5 m. The pendulum is raised to point Q, which is 0.08 m above its lowest position, and released so that it oscillates with a small amplitude θ between the points P and Q as shown below. Draw free-body diagrams showing and labeling the forces acting on the bob in each situation. When it is at point P. When it is at the lowest point. Calculate the speed of the bob at the lowest point. Calculate the total energy of the oscillating system. Determine the height at which the potential and kinetic energies are equal. Describe one modification that can be made to double the period of the oscillation. Explain.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 uniform stick of length L and mass m is pivoted at one of its ends. Derive an equation for the period of oscillation when the stick is set into small oscillation. Answer in terms of m, g, and L as needed.
- A uniform thin rod of length 0.927 m is hung from a horizontal nail passing through a small hole in the rod located 0.082 m from the rod's end. When the rod is set swinging about the nail at small amplitude, what is the period T of oscillation? T = 1.98 Incorrect STwo pendula are shown in the figure. Each consists of a solid ball with uniform density and has a mass M. They are each suspended from the ceiling with massless rod as shown in the figure. The ball on the left pendulum is very small. The ball of the right pendulum has radius 1/2 L. L = 1.6 m Find the period T of the left pendulum for small displacements in s. Find the period T of the right pendulum for small displacements in s.Pr5. A pointlike body of mass m made of lead is fixed inside a homogeneous solid sphere of radius R and mass m at distance R/2 from the center of the sphere. This body is placed on a horizontal rough surface. Find the period of small oscillations of the sphere around its equi- librium position. (The sphere rolls without slip- ping on the surface. The moment of inertia of a homogeneous sphere of mass m and radius R is 2mR* /5.) R/2