Hook 7. L
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A square object of mass m is constructed of four identical
uniform thin sticks, each of length L, attached together. This object is
hung on a hook at its upper corner (Fig. ). If it is rotated slightly to
the left and then released, at what frequency will it swing back and forth?
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- A 200 g mass is attached to a spring with k = 60 N/m and allowed to oscillate with an amplitude of 0.12 m. What is the maximum speed of the mass?A 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 thin uniform rod (mass = 0.24 kg) swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period of 1.1 s and an angular amplitude of 9.6°. (a) What is the length of the rod? (a) What is the maximum kinetic energy of the rod as it swings?
- The figure shows a uniform rod (length L = 2.36 m, mass = 1.9 kg) suspended from a pivot a distance d = 0.27 m above its center of mass. The angular frequency (in rad/s) for small oscillations is: axisA uniform thin rod of length 0.714 m is hung from a horizontal nail passing through a small hole in the rod located 0.074 m from the rod's end. The rod is set swinging about the nail at small amplitude. What is the period T of oscillation? T = SA 500 g mass is hung from a vertical spring and allowed to come to rest or its equilibrium position. As a result, the spring is stretched by 10 cm. The mass is then pulled down an additional 15 cm and released so that it oscillates in a SHM. Find the amplitude and frequency of the SHM and write down the equation of the position as a function of time.
- A uniformly dense rigid rod with mass of 6 kg and length of 0.6 m rotates around its center of mass. Two springs with equal spring constants of 200 J/m2 are attached to each end of the rod (thus there are a total of four springs attached to the rod). What is the period (in s) of small amplitude oscillations of this system?A 1000 kg car carrying four 80 kg persons is traveling over “washboard" speed bumps spaced at regular intervals. The bumps are located 4 m apart. The car is observed to bounce with maximum amplitude when its speed is 16 km/h. The car now stops and the four people get out. By how much does the car body rise on its suspension owing to the decrease in weight?