A particle executes simple harmonic motion with an amplitude of 2.48 cm. At what positive displacement from the midpoint of its motion does its speed equal one half of its maximum speed? Answer in units of cm.

Determine the change in width a, height b, thickness t when a plate is subjected to the uniform distributed load and is made of material having modulus of elasticity e=230 gpa and poisson's ratio ν=1/3. given : a=400 mm and b= 300 mm also the uniformly distributed load in downward y direction of plate is 2 mn/m and in the positive x direction is 3 mn/m and t=20 mm

Air is contained in a variable-load piston-cylinder device equipped with a paddle wheel. initially, air is at 400 kpa and 17°c. the paddle wheel is now turned by an external electric motor until 75 kj/kg of work has been transferred to air. during this process, heat is transferred to maintain a constant air temperature while allowing the gas volume to triple. calculate the required amount of heat transfer in kj/kg.

Two carts, one of mass 2m and one of mass m, approach each other with the same speed, v. when the carts collide, they hook together. assume that positive momentum is to the right. which graph best represents the momentum of both carts over time, before and after the collision?