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
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- A wheel is free to rotate about its fixed axle. A spring is attached to one of its spokes at distance r from the axle. Assuming that the wheel is a hoop of mass m and radius R, what is the angular frequency w of small oscillations of this system in terms of m, R, r, and the srping constant k? What is w if r =R and if r = 0? Thank you for the help. I think I'm tripping myself up with using r in the equations.A ball whose mass is 1.7 kg is suspended from a spring whose stiffness is 6.5 N/m. The ball oscillates up and down with an amplitude of 11 cm. Suppose this apparatus were taken to the Moon, where the strength of the gravitational field is only 1/6 of that on Earth. What would the period be on the Moon?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?
- An object is undergoing simple harmonic motion along the x-axis. Its position is described as a function of time by x(t) = 1.1 cos(3.4t – 1.9), where x is in meters, the time, t, is in seconds, and the argument of the cosine is in radians. Find the amplitude of the simple harmonic motion, in meters. What is the value of the angular frequency, in radians per second? Determine the position of the object, in meters, at the time t = 0. What is the object’s velocity, in meters per second, at time t = 0? Calculate the object’s acceleration, in meters per second squared, at time t = 0. What is the magnitude of the object’s maximum acceleration, in meters per second squared?A meter stick is attached to one end of a rigid rod with negligible mass of length / = 0.787 m. The other end of the light rod is suspended from a pivot point, as shown in the figure below. The entire system is pulled to a small angle and released from rest. It then begins to oscillate. (a) What is the period of oscillation of the system (in s)? (Round your answer to at least three decimal places.) 1 2.340 S (b) By what percentage does the period of the system found in part (a) differ from the period of a simple pendulum 1.287 m long? IT simple - Tsystem! 2 x 100% = simple How is the period of a simple pendulum related to length? Use the period of a simple pendulum and the period found in part (a) in the given formula. %An object on a spring: An object is attached at the end of a spring with no friction. The amplitude of its motion is 50cm, the period 10sec. After 2sec, what are the position, velocity and acceleration of the object?
- A uniform rod of length 2.0 m, and 3.2 kg is suspended from a pivot a distance 0.2 m above its center of mass. The angular frequency in rad/s for small oscillations is approximately equal to: Take g=9.8m/s2. State your answer to the nearest 0.01 of rad/s.Asap plzzxxA ball whose mass is 1.4 kg is suspended from a spring whose stiffness is 40N/m. The ball oscillates up and down with an amplitude of 14 cm. Suppose this apparatus were taken to the Moon, where the strength of the gravitational field is only 1/6 of that on Earth. What would be the period on the Moon? (Consider carefully how the period depends on properties of the system; look at the equation.)
- A 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.A small block with mass m slides along a frictionless horizontal surface with a speed v = with and sticks to the end of a uniform rod (mass M = m, length L = 0.75 m) that can rotate around a frictionless axle through its upper end as shown. :0.4 m/s. It collides %3D a) Use Newton's 2nd law to find the angular frequency w of small angle oscillations for the combined system. b) What is the amplitude (maximum displacement 0max) from the vertical, expressed in degrees?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.