Abrick of mass 4 kg hangs from the end of a spring. when the brick is at rest, the spring is stretched by 3 cm. the spring is then stretched an additional 2 cm and released. assume there is no air resistance. note that the acceleration due to gravity, g, is g=980 cm/s^2.
set up a differential equation with initial conditions describing the motion and solve it for the displacement s(t) of the mass from its equilibrium position (with the spring stretched 3 cm).

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

As a pendulum bob swings back and forth several times, the maximum height it reaches becomes less and less. this is because more and more of the pendulum bob's energy is being transformed into a. heat energy b. kinetic energy c. potential energy d. kinetic energy and potential energy

An ionic compound can conduct electricity when a it is dissolved in water b its crystals are ground into powder c it is in solid form d it is heated to just below its melting point