If both the mass m of a simple pendulum and its length L are doubled, the period will

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Question 13.56 (Please do problem 13.56 only.) A spring with free length 1.2m is attached to a collar of mass of 20kg. if the collar is released from at position A to slide down the smooth vertical rod shown. If the lowest position readed by the collar is A2, where b=2m, determine the modulus k of the spring.

A boat having a mass of 80 Mg rests on the bottom of the lake and displaces 11.75 m^3 of water. Since the lifting capacity of the crane is only F = 550 kN, two balloons are attached to the sides of the boat and filled with air. The volume of a sphere is V =4/3πr^3. ρw = 1000 kg/m^3.Determine the smallest radius r of each spherical balloon that is needed to lift the boat. Neglect the mass of air and of the balloon for the calculation required for the lift and What is the mass of air in each balloon if the air and water temperature is 12∘C? The balloons are at an average depth of 20 mm. The gas constant for air is R= 286.9 J/(kg⋅K)

The following​ mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x1′​(0)=x2′​(0)=​0)in its equilibrium position (x1​'(0)=x2​'(0)=​0) with the given external forces F1​(t)=0and F2​(t)=540 cos 4t acting on the masses m1and m2​,respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies.   m1 m2 k1 k2 k3 x1 x2 K= −k1+k2 k2 k2 −k2+k3   m1=​1, m2=2​; k1=1​, k2=2​, k3=2       Find the resulting motion of the system.   x1​(t) =   x2​(t) =   ​(Type exact​ answers, using radicals as​ needed.)

7. Consider the system shown below. The spring is connected via a cable to the non-rotating shaft of the roller with mass m₂ and radius R. A second cable connected to the shaft passes through the two pulleys. k ww χ M₁ Use conservation of energy to derive the equations of motion. The equilibrium position corresponds to x = 0. Neglect the masses of the pulleys and assume the cable is inextensivle.

Block A rests on a horizontal tabletop. A light horizontal rope is attached to it and passes over a pulley, and block B is suspended from the free end of the rope. The light rope that connects the two blocks does not slip over the surface of the pulley (radius 0.080 m) because the pulley rotates on a frictionless axle. The horizontal surface on which block A (mass 2.50 kg) moves is frictionless. The system is released from rest, and block B (mass 5.00 kg) moves downward 1.80 m in 2.00 s. A)What is the tension force that the rope exerts on block B ?B)What is the tension force that the rope exerts on block A ?